There are 2 ways to update the provider to a different provider for an existing appointment:
Drag the appointment to a different providers calendar.
In the Team view you can simply hold and drag an appointment to a different providers calendar as shown in the images below:
Drag the appointment to any open time for any provider:
Once changed, you will be prompted to confirm the changes to the appointment and whether or not to notify the customer.
2. The other method of changing the provider includes going into the appointment details and changing the provider within those details.
Select the appointment you'd like to change and select the pencil or Edit button
Within the appointment details, you can edit the provided By line and adjust the provider within here.
When finished, you can select the save button and apply the changes to the appointment.