First the event has to be set to allow multiple Team Captains. You can update that setting by following the steps below:
  1. Choose Edit Under "Actions" in the TeamRaiser list for the appropriate event
  2. Go to 4. Select Team Options
  3. Update Option: 4. Multiple Captains on a Team:
  4. Click Save
Then you will also want to make sure to turn on the Team Roster visibility.

Once those settings are updated, the Team Captain will have visibility of the Team Roster within their Participant Center. From there they will have the options to Promote or Demote Team Members to or from Captain.