When you have pets who don’t like each other, it’s best to remember two things.
First, cats are like toddlers in many ways. They have big emotions but not the capacity to think things through. This makes cats very immediate people: If I’m angry, I whap you. If I’m happy, I kiss you.
Second, cats are creatures of habit.
Put these two together and you have the basis of your approach: Create scenarios where they are both happy together, and do it gently and over and over again, and they will become used to being friendly with each other.
One useful way to create positive interactions includes this classic: Feed the cats their favourite food or treat at the same time.
If they don’t know each other, feed one kitty on one side of a locked door and the other on the other side. If they tolerate each other, it’s a plate each, a suitable distance apart.
Your job is to sit down with them, talking calmly. When they’re both finished, you pet the two of them very briefly. Then separate them by picking one up and walking away.
Repeat and repeat and repeat.
In addition, be on the watch for escalating aggression. When they growl or hiss at each other, don’t add to the energy by shouting. If they’re both calm and you know you’ll be OK, pick one up and take it into another room. Give them time to calm down. Then feed them both a treat together.
However, actual catfights can be vicious so you have to be careful. If you think they will scratch, aim at calming everyone down.
Try to break eye contact between the upset cats. You can do this by inserting a newspaper between them.
Talk gently and softly. Give them five to 10 minutes to calm down. Then, separate and reward.
If your kitties are upset and not in a state to be touched, use a soft broom. Lean this gently against one cat's body and push gently. When you’ve got them separated, let them calm down before you have a cuddle and offer treats.