First things first, make sure you know the chord progression very well. It’s usually something based around a ii-V-I but jazz does have the tendency to have a bunch of turn around a in there. Secondly, know your arpeggios well. In jazz its very common to use arpeggios(which ones deoends on the type of jazz you play). Third, theory, lots of theory. I think jazz is one of those genres where a solid theory knowledge is pretty essential. I barely looked at music theory before I started playing jazz. And as a bonus it makes playing any other style easier to when you know theory.lastly listen to a lot of jazz(that’s honestly how I do my gypsy jazz improv). Why does listening help? That basically helps your ear recognize the kinda stuff you like to play over a similar chord progression and realize the things that make it jazzy. For just straight up jazz(so no gypsy jazz) I would recommend listening to Wes montgomery. He is very tasty with his jazz playing so that may give you some ideas.