As soon as you change firms, it is important to submit the transfer to REBNY. If this is delayed, your listings with your new firm will be rejected.
To update your associated firm, you need to complete another REBNY member application (same as what you completed for your past firm). Make a note on the form that you are a current member, and include your REBNY ID. If you are paid up for the year, you do not need to pay again.