Adopting a dog that is not a puppy is just fine
In fact, they may get along even better. The only advice I can give you is to make sure that you introduce them to each other on "neutral grounds." By that I mean, not your house or the other dog's house. That way, neither one of them feels like they have to protect their territory. Make sure they get along. It might take a couple of weeks for them to get used to each other, but hopefully, they will get along great immediately
I think it's wonderful that you're trying to adopt a 4 yr old. Are they both spayed/neutered?