No, you just move your sim to the new phone or get one from an O2 shop as if it's a different size they sort out a sim swap for you.
Your old contract is cancelled by the new one.
Which models are the old and new phones?
The S2 has a standard sim, you will need a micro-sim either call O2 for one or go into an O2 shop and they'll sort you out straightaway.
If you get one through the post use the sim swap page here: