Cats are very territorial and often introducing another cat into the household can cause problems.
It is always a lot easier, if you prefer to have two cats, to get them both at the same time as they’re likely to get on a lot better if they are introduced to the house at the same time rather than one having the run of the house first and then having to share it with another later.
After the initial few fights that the young cats might have, they should tend to get along well with each other and enjoy each other’s company in play and relaxation.
When a kitten is introduced to the house of an older cat you need to make a determined effort not to neglect the older cat.
This is very easy to forget when you’ve got a new kitten as people tend to fuss over kitten a lot more than older cats and it is not uncommon for the older cat to become jealous and start fighting with the new member of the family.
This can lead to other cat behavior problems where a house trained cat might decide to start urinating in the house where it wouldn’t have done so in the past, or it might go off its food and stop eating and get sick.
By considering the feelings of the older cat, not neglecting it, giving it sufficient time and letting it know that it is still special, there is more chance that the new kitten will be accepted better by the established cat.
It is made more difficult when the cats are in confined living conditions, and where possible, if there is conflict try to keep the cats apart for a while until they become used to one another.
You can put their litter boxes in different areas of the house, and also keep the food dishes apart.
Any time that one shows aggression to the other, calmly step in between and stop it going any further.