Do not leave your puppy alone with the older dog for the first several weeks after bringing her home. Give the two of them time to establish a firm relationship before you trust either of them to “follow the rules” without your supervision.
Unfortunately, the happiness of bringing home a new puppy can be dulled when you realize your older dog doesn't share everyone else's excitement. While it's true that dogs have a pack instinct that may make it natural for them to accept new family members, they also have territorial instincts that can be threatened, even by a puppy. However, there are several things the concerned dog owner can do that will make the transition time to a two dog family easier for your older pet.
Socialize your older dog by taking her to the dog park or other safe environments where she can meet smaller dogs. An article published by gopetsamerica.com states that older dogs that are not already socialized will have a much more difficult time accepting a new dog of any age into the house.
Bring home a blanket or other item with the new puppy's scent on it. Allow the adult dog to play with the item and get used to the new smell. It is also a good idea to bring a scented item to the puppy.
Allow the dogs to meet on neutral territory before bringing the puppy home. Approximately one week before bringing the new puppy home, arrange for the older dog to meet the puppy at a park or anywhere that is not his home territory. Lavish the older dog with affection and assurance as he sniffs and greets the new dog. Take them on a walk together if the puppy is old enough to be led on a leash.
Purchase the necessary items for your puppy before she gets to your home. Do not expect your older dog to share food dishes, bedding or toys.
Maintain your older dog's schedule as much as possible. Although a new puppy demands a lot of care, do your best to continue walks, play time and meal time with your older dog in the way that he's used to. The new puppy should be taught to adapt to the existing household schedule and not vice-versa.
Supervise the play time between your new puppy and older dog. Don't assume that they will "work it out" between themselves. Both dogs will need you to fulfill the role of strong pack leader and enforce the acceptable boundaries.