Treat a second dog as if it is your first dog. Second dogs are more likely to show aggression to other dogs on a walk than first dogs so get your puppy out walking on his own and meeting other dogs as much as possible. Spend time training, playing with and grooming your puppy without your adult dog present. Build that individual bond with him.
Play with, groom, walk and train your puppy without your adult dog present. You need to be more important that the adult dog to your puppy and in order to do that you need to build an individual bond with him.
Your puppy must respect his elders. It is not appropriate for your puppy to pester an older dog simply because your adult dog won’t tell him off. If you don’t discipline your puppy he will become like a spoilt child and sooner or later he will get into trouble out walking when meeting other dogs. Intervention between your adult dog and puppy needs to be frequent and consistent. Stopping the fun is enough. Don’t punish your puppy. You need to be the referee particularly if your adult dog seems to be too tolerant.