No other pieces. You will use the existing safety mechanism detent ball, and the safety mechanism spring. Parts 49 and 50. They are held in place by a safety mechanism spring retaining pin, part 51. Don't lose it. It takes a very small punch to tap it out. Also, be careful not to lose the small spring and even smaller ball. Remove the above mentioned parts, remove the safety from left to right, put in the new one. Drop the little ball back down the hole, then the spring, then use all three of your hands to keep the spring down, then tap in the pin.
I've always found replacing the safety and re-assembling much easier than finding the little spring or ball that I've never yet failed to drop on the carpet. (I have a magnet)
If you order another safety, you might consider a jumbo for a combat shotgun and it wouldn't hurt to have an extra pin, spring and ball if they aren't included.
If you're changing out the safety anyways I'd highly suggest one of the extended safeties from Vangcomp. head and shoulders above the stock, and superior to the Scattergun Tech safeties. One of those and a Vangcomp mag follower are two of the best bang for buck improvements you can get for an 870 IMHO.