Let me offer a few ideas, take all with a grain (or more) of salt depending on your industry/country/culture/team makeup/ages, etc.
One of the best ways I've seen to get a new team member to have their voice heard and to be able to provide feedback from a different perspective without implying any criticism is to set up study sessions (be it presentations, small seminars, workshops, etc.). Every new member to a team coming from a different background has some cool things that they've learned that everyone in the team could learn about. If you explain to your team (and to the new member) that you want to set aside an hour a week for one team member to lead such a seminar/presentation/study session, you can use that as an opportunity for your team member to speak freely.
This will require three things from you (assuming you are the boss):
- Setting aside time to do this for you and your employees
- Encouraging members to share more than 'this is what I'm working on' (to the point of suggesting themes if necessary/appropriate)
- Making this feel 'valuable' for the people attending
- New team member's knowledge is acknowledged and respected
- 'Education' is much less threatening than 'Suggestions for Improvement'
- People actually learn cool stuff and get to share cool stuff (e.g. a member of my team recently shared information on how to read through corporate reports, and then showed various competitors in our industry and where they stood on each metric -- it was totally outside the scope of our usual work, but totally awesome to learn about!)
- Takes time
- If employees aren't motivated to learn/teach, it will fall flat
- New member (depending on personality) may feel 'put on the spot'
- Requires a lot of really good coordination from the manager (or key team members) to be successful
Encourage 'Why?' Questions
Again assuming your are the manager, you can ask your new team member to provide you with a single 'Why?' question about the work process every week. You can explain this with fancy manager-speak making this sound like a noble quest, or you can be honest with them. At any rate your goal is just to get them to ask a good 'Why?' question, without showing any judgment or criticism.
If the question has an answer ('We need to send out those company-wide e-mails on properly disposing waste because it is required in ISO-14001 for our certification') you can give it, and if it doesn't have an answer, you can use that opportunity to brainstorm with them about where the gap is. So long as you aren't critical of them when you have the conversations, they should be more than happy to share.
- Quick and easy to implement
- Requires little time
- Aids in employee education
- The employee may be really bad at coming up with good 'why?' questions
- Depending on their attitude/your attitude, it could become a bit controversial (they ask critical questions, you provide critical responses)
This is my personal favorite. In Japan they hold a welcome party called a 歓迎会 (kangeikai) where you get the new employee and the team drunk and ask them questions about their last job, their family, etc. This is probably not legal in most of the world (and probably wouldn't go over so well in the US at least). In the UK your non-manager employees will take you out to a pub for a pint or three and get to know you as a person.
In both occasions, the benefits of alcohol aiding otherwise awkward social interaction is that the new employee becomes less threatening to the group because, well, who looks so threatening when they're teetering at the bar?
(this is also a tactic used in Korea/China to get you absolutely plastered the night before a negotiation, and make you utterly useless in the morning. Alcohol is truly a multi-purpose tool for use in business.)
Of course this doesn't work for every country, situation, etc. And it likely won't solve everything. But it's a good start.