Hi John. The answer to your question revolves around how social the adult dog is. If she’s good around other dogs, there should not be a problem if you avoid them having treats, toys or food when together (basically anything worth fighting over). Of course, puppies can be annoying even to ‘normal’ dogs so supervision is essential. Hopefully, the puppy is crate trained so this can be used for time out for HER when needed or a place to separate the dogs for feeding.
On the other hand, if she’s not completely comfortable around other dogs, then a puppy will be very hard, as they tend not to respect personal space. Therefore, my advice is to temporarily settle in the adult female and assess her with other dogs first, and then decide if the puppy can be reintroduced. The answer is likely to be yes, as long as you do it at her pace.