If you just fitted a rear sprocket without replacing the front and the chain, you are very soon going to have to replace all.
An old chain will quickly wear out a new sprocket, and stretch more to accommade it.
Just think what the back sprocket will try to do, it now has a chain which does not ride well, so it tries to manipulate it to suit.
The worn front sprocket now fights with the manulipated chain, trying to make it fit itself!
Then the chain hits the rear again, and the whole process starts over.
The chain and sprockets take excessive punisment, resulting in premature wear and maybe breakage.
The chain and sprockets will not know if they are Arthur or Martha, and the process of wear will go round and round in ever decreasing circles, until it eventually dissapears up its own butt.
If you intend doing it, invest in a case saver!
Golden rule, always replace all, never mix and match chains and sprockets. It is safer, and in the long run cheaper!
Buy a larger front sprocket and a chain to suit, and you will have 2 good sets.