So long as YOUR FFXIV lisence is tied to YOUR PSN account you can play from any PS3/PS4. (note that PS3 and PS4 themselves are not interchangeable, I just don't know which you have. So in short if you have a PS3 License you can play on ANY PS3 but not PS4. If you have a PS4 License you can play from any PS4.

Sorry if it comes off like I'm talking down to you. I just wanted to make it as clear as possible and there is a lot of confusion around this subject. Especially once PS4 entered the mix.