How to stop my dog's aggression towards my newly adopted dog?

In addition to a gradual introduction or acclimation, consider using a pheromone product such as the Adaptil collar or DAP plug in diffuser. Either may decrease any anxiety or aggression. Correct any aggression or negative behavior immediately. Praise and reward good behavior. Be consistent and be patient.

You will likely need to separate the new dog from the 2 "older" dogs for a period of time. Spend time with each separately, but make sure that they cannot see the new dog, i.e. keep him in a separate part of the house behind a closed door for at least one to two weeks. Then you can allow them to see each other, but not have contact. Move slowly, from this phase on to allowing them to see and smell each other across a barrier such as a baby gate. Finally, allow them to spend supervised time together. Reward good behavior with high value food treats (i.e. bits of cooked chicken) and go slow.

It may take some time for her to accept him. If she is being aggressive toward him than you should not allow them to be together unsupervised, espeically around feeding time or any toys/bones that she may protect. Give her extra attention, praise, and treats while the puppy is around so she knows he is not there to replace her. You could also try an Adaptil collar or diffuser and see if that helps. If she doesn't start accepting him than you could talk to your vet about trying an anti-anxiety medication, like Prozac or Trazodone and see if that helps.

Gradually increase the amount of time they are physically together as long as there is no aggression. Correct any negative behavior immediately. Consider a pheromone product, such as the Adaptil collar or DAP plug in diffuser, to decrease any anxiety or aggression. Provide additional bowls, toys and blankets to prevent resource protection. If the behavior persists, consider a consultation with a certified veterinary behaviorist.

WIth some patience and training, they may be able to get along. Consider a pheromone product, such as the Adaptil Collar or DAP plug in diffusers, to decrease any anxiety or aggression in the home. If you have cats, use Feliway Spray or plug in diffusers. You didn't specify the species in the post. Keep them separate, then gradually introduce (or re-introduce) them. First, allow them to hear and smell one another through a closed door. As they progress, you can allow them to see one another but without physical contact. Correct any aggressive or negative behavior immediately. The next step would be to place one of them in a closed carrier and leave them in the same room. Do this for ever increasing periods of time until they are acclimated. Finally, allow short, supervised playtime. Be consistent and praise/reward good behavior. Separate them if they get "rowdy" until they settle down, then reintroduce them.

Introduce them to one another gradually. First, by allowing them to hear and smell one another through a closed door, then by sight without physical contact, then supervised contact. You will need to progress gradually through each phase. Correct any aggressive behavior immediately and praise good behavior consistently. A pheromone product, such as the Adaptil collar or DAP plug in diffuser, may decrease any anxiety or aggression.

A gradual introduction would be recommended. Separate them for a few days, then begin anew. Jackson may eventually become acclimated and accepting of the new dog, but it could take time. Consider a pheromone product, such as the Adaptil collar or DAP diffuser, to decrease any anxiety or aggression. Correct any aggressive behavior immediately and praise and reward good behavior.