My team lead is leaving the company, there are currently three people in the team including me. The other two team members are both more experienced and better qualified than I am, but they aren't interested in doing anything other than technical work. They enjoy being given technical tasks and problems to solve. That's also what I do, but I like being involved in project planning and setting the direction of our work (the team lead does this with some input from the team). I would like to progress and be able to lead the team and set direction on certain things - using direction from management and the technical opinion of the team in addition to my own technical skills.
The rest of management are either of the opinion that there is no need for a new team lead OR they are looking to recruit a new team lead externally (I don't know for sure yet).
Should I wait for the position to be advertised and then apply for it? Or should I tell the department management that I'd like to progress? What kind of wording should be used? Should I use the outgoing team lead? I have a good relationship with them.
I am nervous because the rest of the team have higher titles and more qualifications than mine, I don't think anyone expects that I could do this job or would want to because the rest of the team doesn't want it, but I do think that if I had the opportunity I could improve our work. Plus, I was due a much needed pay increase that got put on hold because of the pandemic and this could be a good way to increase my salary.