There are 2 approaches to introducing cats - gradually introduce them or just put them together annd let them sort it out! Although I favour the first in theory, I used the second when I got Mosi because keeping 2 cats separate in a one bed flat is not easy. Bear in mind that disagreements between cats tend to sound worse than they are with lots of fluffed up fur and hissing but rarely much real aggression. Sometimes I think it's worse if they can see or smell another cat but can't actually make any contact.
What I did when I got Mosi was to keep Jaffa in the bedroom to begin with whilst Mosi made himself at home in the living room/kitchen area and found (and used) the litter tray. After several hours of that, and going back and forth between the 2 rooms, I took Mosi in to Jaffa and just put him down beside him. They both hissed at each other (the only time I have ever heard Mosi hiss) but after a bit Mosi decided that Jaffa was ok and Jaffa decided that Mosi was ok as long as he kept his distance. Any time Mosi got close Jaffa would hiss at him and over the next few days they gradually got used to each other. Jaffa still hissed at Mosi and would sit on him in dominance (Mosi kept trying to play with him) but Mosi has never been the kind of cat to let that bother him. Gradually the hissing stopped and they learnt each other's boundaries (well, Jaffa tried to teach Mosi the boundaries and Mosi constantly tested the boundaries!). So pretty successful intro but there was a fair bit of fluff on the floor at times and sometimes it sounded a lot worse than it was.
Alternatively keep them separate for longer and exchange scents by swapping blankets etc. then gradually introduce them leaving them together (supervised) for short periods of time.
Whichever method you choose, try not to intervene at the first sign of trouble unless either cat is actually getting hurt or seems genuinely distressed. They will need a bit of hissing and scrapping to sort things out. Plus your 4 month old will probably want to play all the time. Whilst play between a kitten and an adult cat needs to be supervised to make sure the little one isn't getting hurt, sometimes it's better if the adult cat is allowed to show the youngster who's boss and what will happen if he over steps the boundaries. Sometimes separating them just as that is about to happen just delays things. I used to worry that Jaffa would hurt Mosi simply because he was so much bigger (he's a big cat and Mosi was only 14 weeks old) but although he would sit on him and pin him to the ground, it was clear that he had no intention of causing physical harm.
