What to do with old iPhone SIM card?

I dropped my iPhone 4s in the toilet at work and I was able to get another phone but I have to ship the old phone back, I have no clue if I should put my old SIM card in the new phone or just leave it in the old phone before I ship it back. I know this is probably a simple problem but I've never had to deal with this but I don't know what to do

You can keep your SIM card if it has not been damaged by the water. Clean it with some alcohol to evaporate whatever moisture that may still be present.
Use it in another phone if you wish.

Ultimately, I would ask for a new SIM with the new phone and once it arrives call your carrier and do a sim swap.
That way you know that you have a new and undamaged Sim card.

The SIM is yours. Your number is on it, as well being the number most know you to be reached by. So you keep that.