While each bank has its own specific changeover requirements, the rules for adding an authorized signer or switching a signer are generally the same across institutions. You should check this procedure with your bank.
Your Bank may not necessarily be able to accept all signatories on your account and may carry out certain checks and procedures.
They will contact you when your new signatories can start signing on the account. Any missing or incomplete details may result in your application being delayed.
An account must have a minimum of two signatories and these should always be current committee members. In most cases this would include the President and Treasurer.
Generally Banks will require current signatories of an account to complete a change of signatories form or write a letter to the bank holding the checking account informing the bank of the change in signing status and confirming the new signer on record as representative of the society/group.
You should present this form/letter, as well as the minutes from the organization's meeting confirming the new signer to the account, to a representative of the bank in person.
Have a meeting where it is documented the current President grants access to the new Treasurer and President, and access is removed for any outgoing personnel. Print out the minutes of the meeting as you will likely need to provide these to your bank as evidence.
Changing signatories could take a number of weeks, so it is important that this meeting is held in advance of the end of the academic year, before any committee members leave or graduate. The Bank may need to still contact all individuals directly.