Slow and gradual introductions over several weeks lead to the best results when introducing a new cat to a resident dog.
For first introductions, keep the dog leashed and give them brief, supervised meetings to sniff each other in a neutral room.
Use treats and praise to reward calm behavior and positive interactions between your cat and dog during meetings.
Give each pet their own quiet, off-limit area with food, water and litter box access to retreat to if feeling overwhelmed.
Expect some uneasy interactions at first. Give your pets ample alone time and don't force interactions. They'll need time to adjust.
Don't leave your cat and dog freely interacting alone until you're 100% confident they've established a friendly relationship.
With proper introductions and adjustments, most cats and dogs can learn to coexist peacefully in time. Go at their pace.