Could you give us more information? Like the genders, the previous exposure the 7 yr old has had to other dogs, the reaction the old dog has to the puppy, etc.

Introducing a puppy can sometimes be harder on an older dog. For the first few weeks at least I would not leave them together unsupervised. Since its a puppy though, I would crate train and not leave him/her alone with the older dog for months, if not longer. Make sure the older dog doesn't have to share anything at all. Both of the dogs need individual bonding time with the humans and also supervised play time with each other.