Older cat and newer cat fight

I have a 7-year-old female (spayed) female cat and in the summer, we took in a kitten off the street, which at the time was around 4 weeks old. We took time introducing them and all seemed well, until he got bigger and wanted to play more. He jumps on her (I believe he is just playing), but she growls at him, hisses, makes this very loud growl/meow like she is fighting him and she runs from him every chance she gets. It's like when he comes around, she puts herself on guard with the tail flicking and low growls; but, when he is calm and just wants to lay down, sometimes she will allow him to lay beside her with no problems. Then again, sometimes she will go up and swat at him for no reason, as if to remind him that she doesn't want him around. Any suggestions?

It sounds like your resident cat, (the 7 year old), and the new kitten are still establishing where they stand with each other.

It's normal behaviour when you introduce cats. Give it time and don't yell or punsih them.

Only step in when things get serious when someone is going to get hurt. And even then, use a dark heavy blanket to throw on top of them to surprise them and distract each other from what they were doing. Then take each cat to separate rooms for a shirt time out session, (say five minutes).

Bunny kicking, hissing, growling, twitchy tail comes with the territory when introducting cats. Just do a search on "Introducing cats" and plenty of threads will come up.