Bringing home a new dog or puppy can be tricky for your current dog. Especially if your dog is used to being the sole recipient of all your attention. Introductions can be tricky.
If you can find a safe neutral place to introduce the two dogs other than your home, that would be preferrable. Although if it is a puppy that is not properly immunized, take precautions to find a safe environment that has not been used by unknown dogs that could possibly spread disease.
Rub a soft cloth on the new dog’s rear end and let your dog get a good whiff of this new scent in advance. This will give the new dog a familiar scent when he is introduced.
If your current dog is curious to see the new pup but then walks away, let him. This is a meeting that should be on his terms so don’t force a social encounter. If it’s too stressful for him, walking away is a good decision for now.
Make a big deal about your older dog when your new puppy is around. New puppy entering the room means lots of attention for the older dog so that he is not losing attention to the new dog. Setting up a positive association with the new pup is essential.
Make sure the older dog can get away from the puppy. Puppies typically want to follow other dogs around and at times can be a nuisance. Give your older dog space where he can go that the puppy cannot follow, or redirect the puppy away from the older dog if you think he needs a break.