The current Account Owner (aka primary owner) will need to go into their Team Members settings to make the change. At the top right-hand corner of the screen, there will be a button that says 'Make Primary Contact'. Click that to delegate your account rights to the new owner. An email will be sent to the individual's email for their action.
Do note that the Primary Contact status will only take effect to this team member once they have accepted the request sent to their email. Until then, you will still hold the Primary Contact (i.e. Account Owner) role.