Yes it's possible to get a relapse of the cold after you've already had a cold.
However when you do get a relapse of a cold you typically will not get infected with the same cold virus as you had before.
There are many different types and strains of the cold virus that people can be infected with.
When you do get infected with a cold virus your body then usually becomes immune to that particular cold virus so you shouldn't be able to catch that same cold virus again.
But if there's another cold virus going around and you haven't gotten that cold virus then you can catch that cold virus.
So yes it's possible to catch another cold and have a relapse of the cold virus even after you've gotten rid of one already.