You get free banking with TSB if you transfer in 1, 500 per month. Once you do that you can transfer money online to any account for free. I'm assuming you're not transferring to an AIB current account, as this account could cost you fees to have.
You don't have to close you AIB saving account at all if you wish. You can have savings accounts at any bank, you don't need a current account with them. Close saving accounts only if you get a better. rate elsewhere (possibly not PTSB)....take a look at the savings best buys thread