I'm using Apple Pay and I recently canceled my card. Interesting thing is that even before I had my new card Apple Pay switched to the new one, I didn't have to do anything. I wonder how they did that.
Credit cards send updated card information to various merchants that you've used. Usually it's for things like subscriptions or bills so you don't have a gap in service. Personally I hate it because it lets smaller stuff slip through the cracks for longer.