I think Judy Knight has a great response.
What I would add are a couple of things. First of all, once a team loses or adds a member it is a "new" team. The questioner's description of changed teams, blended teams etc., really means starting over. The good news is if staff have had positive team experiences they can bring their team skills and talents to table. Therefore the teams are really beginning again in the new environment.
Secondly it sounds like there has been some significant changes in the organization over time. Staff may be feeling losses, insecurities, (sometimes survivor guilt) and we have found that acknowledging the transitions is very important A facilitated meeting that focuses on where we have been, where we are now, and where we are going that also provides an opportunity to celebrate prior successes and to "mourn" losses can be very powerful. New team members can participate and learn a great deal in the process and begin to form the interpersonal glue that effective teams typically demonstrate.
An additional issue is that of interdependent teams and how to create good collaborations. Spending some up front time defining the benefit of collaboration, the downsides of collaborations, the expected "bumps" in the road as well as approaches to minimize challenges and support the work is well spent time. Just jumping in without the pre-requisite planning usually leads to difficulties. Our experience also suggests that the support and modeling of the senior teams is absolutely essential.