Bringing a new pet into a new environment can be stressful to everyone (humans, current pets, new pet, etc). It is important to give time and space to all pets in the environment - to allow them to decompress. This helps them learn about the new situation and environment without having to react. They can become more comfortable and aware of what will be expected from them. This article talks about fostering but is just as important to adopters and even those who have multiple resident dogs that aren't getting along.
Introducing Dogs: It is also important that proper introductions are done with resident and new canines. This will help set the pets up for a successful relationship.
This article gives tips on things you should do prior to bringing home a new dog, things to be aware of, and additional tips:
Canine body language and introducing dogs to each other:
How to introduce dogs to each other on a walk can be read here.
Have lots of high value treats (diced up chicken, string cheese) both dogs are getting high rewards every few seconds. Calm praise, create distance between dogs if you sense tension or hard stares are building.