when bringing a new kitten or cat into your home do not automatically introduce it to your other cat(s) in your house. First let the cat roam round the house sniffing out its new surroundings. Wait about 10-15 minutes, now its time to introduce them to there new family.
When approaching another cat it depends on how friendly that cat is with you and the sex of the cat can play a major role in behavioral issues. I found out through my own experiences that females tend to adapt quickly compared to male cats. Afterward place the new kitten/cat with the one(s) already in your home , in the same room and stay with them and continue to pet/play/introduce one another. After 15-30 minutes of bonding, its now time to adjust them into the daily routine of your lifestyle and their’s.
Put out some food & water for all the cats in your home. see if they come and eat side by side, if not just bring which cat is missing and place them side by side, once each cat has remained calm and are now eating together this is a good sign that each cat is relaxed and not stressed or jeleous that you have brought someone else into our home. After eating the cats ill probabl go there separate ways to clean themselves and maybe take a nap, once settled into the new surroundings and the cats have been introduced to the cats and have been fed together,the next couple of days they will hopefully start to play with eachother,etc.