Once your Caltech email address is no longer active, you are able to downgrade your PRO account to a free one. The data already in your account will not disappear but future usage will be limited by number of projects and possibility of sharing with collaborators. If you want to continue with a PRO account, try one of the following:
Check with your new institution to see if they have licensed Overleaf PRO. More and more institutions are jumping onboard -- Stanford, Purdue, Virginia Tech, etc. The full list is kept up-to-date at overleaf.com/universities
Sign up for an individual account: the various plans and prices are also online at overleaf.com/plans