There is no "switch team" option for contracts, but you can add someone to a different team and remove them from the original team (or keep them in both teams). If you have any open contracts, you should coordinate with your freelancers and agencies on moving the contracts.
To move a hired freelancer from one team to another
To add a hired freelancer to another team while keeping them in the original team
- Rehire the freelancer into the new team -- you can have multiple, simultaneous contracts
To move a colleague team member from one team to another
- Get the email address associated with the person’s Upwork account.
- Go to Settings › Members & Permissions
- Choose the new team in the selector
- Click the Invite New User button
- Fill out the form
- Switch to the old team in the selector
- Find the team member you want to remove
- Select the checkbox in the last column
- Click Remove from Team
You can also keep the team member in both teams by skipping Step 4, above.