
There are no guarantees about how two dogs will eventually (once adults) get along. As a general rule, males get on with bitches best, but the bitch will have to be spayed of course assuming the male is entire. And even castrated males have been known to mount and tie with a 'willing partner'. As a general rule, and there are always exceptions, I'd not pair two terrier males together under the same roof. But this is really all down to how much in control you are. Provided you are there most of the time (great!!) and aware that the puppy will have no respect for the older dog it should be perfectly possible to have a new puppy in with an older established dog. Adults usually know not to attack puppies, but if pushed too far and not seeing you take charge, may. They know that puppy teeth hurt!! I'd recommend using a crate, or other specially made area to have the puppy until you are right there to supervise what's going on, make the introductions. Ideally introducing two new to each other dogs, should be done off the property, bringing them home together. But obviously that can't be done unless the puppy is fully vaccinated. So set up the place for the puppy before you collect him. And actually it might be a good idea to have a crate in the car for the puppy, and take your existing dog along with you so they can 'meet' in the back of the car, but not together. If you leave the other one at home, when you first arrive, take your new pup to the back area to empty, and then carry him in to his crate, having your existing dog in another area while you do this.
Don't feed them together to begin with - food is a trigger and puppy will dive into the other bowl, given the chance. They need to be able to play together, but the moment things get too manic, separate them again. And always be ready to step in if necessary.
If your existing dog is still a puppy - wait. It's better for the first dog to be over a year before taking on a second puppy.
FWIW, we had two male Bassets, 10 months apart in age. originally. Yes there were the occasional spat, but I was home all the time, and they generally speaking, got along fine. On the other hand, my friend had two male Bassets, litter mates - nightmare. The only time they'd be okay together was out on exercise.