Team lead can be a lot of different things, so I'm going to throw out some basic assumptions for your office:
Someone contributes to the decisions and documentation regarding how well people do their jobs, and what the reward/penalty should be - that includes performance reviews, raises, incentive pay, promotions, the granting or revocation of official privileges (for example sometimes only top performers can work at home). My bet is that as team lead you can influence these decisions, but you are not the actual decision maker
The project manager has overall accountability for the cost, schedule and deliverables of the project and at what quality level the project is completed.
As the team lead, your core area is to be a subject matter expert in how the work should get done, whether your team has the resources they need, and the tasking of who does what within your sphere. Resources are probably both internal things (like experience, knowledge and skills) and external things like access to tools, equipment, access rights, etc.
The reason I highlight this is a key to using power is to know what power is really yours. If I'm right in the basic assumptions - a key area of your power is deciding who gets to do what in their role. There's generally choice work that is more exciting and then some boring stuff that no one is thrilled about. That's a real non-monetary driver.
Here's a few different strategies varying from very gentle to a bit more aggressive.
Reward good work
It sounds like you've got some team members with a fine attitude and some with a problem. Make sure that those who are working well get rewarded. In particular, if someone has proven themselves to be diligent, hardworking and honest:
Don't second guess their judgement. It's OK to ask questions so that you understand a situation, but don't second guess someone who's proven that they can perform in terms of time estimates or how hard something is.
Give them your time and attention when they ask - make sure that folks who are performing are a priority when they have an honest issue.
Talk to them about what they like doing, what they want to do and what their ambitions are and try where possible to give them appropriate and challenging assignments.
Keep them in mind for good opportunities like training or a chance to try something new.
It's not "privileged" treatment if you are rewarding good work. When a non-performing team member asks for or demands similar rights, return to the behaviors that have been a problem and point out that you're not OK with giving them new opportunities when they can't finish current work on time.
Don't Join In
Seems obvious I know. But don't contribute to the situation - don't make a habit of long chats, and don't let a meeting time slip because of chatter. If you've asked once for people to get to the meeting, walk into the meeting area, close the door and start.
Know and make clear the difference between asking and telling
Asking for input is good - as a team lead, you won't know everything about how the work gets done. Ask the team for honest assessments of scope and possible impediments. Feel free to question things that seem crazy, but do ask.
But draw a line between the asking part of the conversation and the telling. If you have a specific task and a hard deadline, this is a job requirement, not a favor or a polite request. The company is paying the employee and in return he's agreed to do this work. Make sure that when you give a task it is clear that it is an assigned thing, given clearly and with a deadline. "I need this by X date" not "could you do this by x date?", "I'd really like it soon, OK?" or "how about this thing by around this date maybe?" Being clear and direct is not being a jerk, it's avoiding ambiguity. That's your job, and for many people it's a relief to know exactly what they need to do and when.
You can even reinforce it by writing it down - if you meet in person, follow up with an email that says each assignment, so it's written and unambiguous. If you're having a real hard time getting follow through, CC any member of management you need - the Project Manager, the bigger boss, who ever it takes. That way the person can see that not only are you telling them what to do, but all parts of management see it too.
Collaborate with the Resource Management
You've got some bad performance behaviors here. Check in with who ever IS the resource management (the person doing reviews, figuring out raises, etc.) and give the feedback of your issues. Be very sure of how this feedback impacts the success of the project. Just because someone is annoying is not a good reason to complain, but when social conversations + an unwillingness to compensate with longer hours leads to slips in project schedule - there's a problem. You can certainly give feedback directly to the people who have the problems, but when you've done that once or twice, it's time to go to the resource manager and get help.
If you ARE the person writing the reviews, get a check in with your boss on how to proceed both with writing the review and with follow on action.
The key here is to have the people with a problem realize that you are not a lone crazy person - you are part of the management structure and behavior that leads to slips in productivity are a company problem. Just because you are new and unknown does not mean your perspective is invalid, and if the company believes in your abilities as a manager, the rest of the managers around you should be able to back you up.
Stand up for yourself.
I have NEVER found it necessary to yell, bang my fist, stomp around or be otherwise angry and authoritative. What I do find is that I must be clear, honest and direct while remaining in control. There's different language and formats for this based on whether you are dealing with a public situation or a private one on one conversation - but either way, there should not be a reason to raise your voice. I strongly advocate being factual and directly tying the problems together. Here's some examples:
Do Say: "I've been listening to this conversation for half an hour, you all started at 10:30 and it's now ll. I've also seen it happen 4 out of 5 days this week. I know you all want to leave on time, but have to get work done."
- Don't say: "it seems like you guys have been talking for ages. This happens all the time. Can we please get some work done?"
Do say: "we agreed to this deadline three weeks ago. We've talked about it every week, and every time we talk, you say it's all good and you're making progress. Now we're three days from the deadline and this is the first time I hear it can't get done in time. I understand the need for personal commitments, but at what point can you make finishing this task a priority?"
- Don't say: "hey, we've known for a long time that you had to do this. Can't you get it done this week?"
On some level, there is a point where you are basically saying "I'm the leader, and I have authority. You can do what I'm asking from you, or I can figure out how to get you out of my team and probably out of this company - what you do from here is your choice." Put this way, it sounds like a threat, but it doesn't have to. Simply asking for what is needed, calmly and clearly can generally be enough.
If you don't get emotional, you have a much greater chance of the employee not getting emotional either - shouting matches have to get started by someone - don't let it be you, keep cool. If the employee starts the shouting, ask them to stop. If they won't, disengage the conversation and suggest that you continue it when they have cooled down. This is not very far from dealing with a child who is throwing a tantrum - don't add to the emotions with your own input - demand and expect mature behavior and make it clear that calm behavior is a requirement.
If you see a bad pattern, you will likely have to express this in a private conversation. Often performance problems are not a single bad day or occurrence but a pattern of not getting enough work done over a long time span. So what becomes necessary is to put all the observations together and then direct the focus to getting tasks accomplished. Once you get into this zone, you need to be crystal clear yourself on what your authority level. Sometimes a team lead is not allowed to have a conversation this direct, if they are not the supervisor of the employee.
When I have a performance issue, I take an obsessive number of notes. The only way I can be precise with people about a problem in a pattern is to actually know the pattern. So when I have periodic checkins in a problem area, I have notes on when I checked in, with who and what they told me. When I have repeated issues with long chatter and frequent personal life conflicts - I start saving emails and making a note about the chatter start time/end time.
While I normally am not precise on details, the ability to give specific honest feedback is really important and worth the effort when there's a problem. We all gloss details so it may very well be that the people with problems don't even realize why there's such a big issue.
Asking your boss
Some of the politics above are not clear in all offices - but the person YOU directly report to should be clear. I'd advocate going to your boss at any time - they are always a good person to ask on office culture and politics stuff, and the issues here the types of team change/growing pains that can take a bit of coaching for a new team lead. It's entirely appropriate to ask for help, get vetting on your intended next steps, and to report on issues that are brewing.
Things to consider:
- It's never bad to have a plan in mind. Even if your plan seems rather crazy, at least it shows you are trying and that you are taking responsibility.
- Most management advice will require that you make the words your own. Many bosses will give you examples of ways to approach the situation - realize that repeating the words verbatim is almost never a win - if you believe in an approach that your boss offers, make the words your own, so that you are speaking from your own beliefs.
- There may be do's and don'ts in how the company would like you to deal with issues - be clear with your boss on when you MUST handle something in a specific way (or MUST NOT handle it in a certain way), and when he's merely offering you an option. It's OK to ask point blank - "is that an order or an option?"