I don’t know much about your buns — so I’ll start off by asking if they’ve been properly bonded? Or is this just behavior that has been happening because you stuck them together with no official bonding process?
I mean, if you didn’t do official bonding then this is really good behavior! But I would suggest going back through a bonding procedure which will most likely strengthen their bond more to help with any of this behavior. For example, right now I’m bonding one bun to my already bonded trio of bunnies. They’ve been doing pretty good in a small space but when I open the space up larger then they go back to chasing and so forth. So I have to reduce the space until their bond is more cemented in the smaller area and then try again in a bigger space.
Also, is he nipping when he chases? I wouldn’t be too worried about JUST chasing unless it seems to be really stressing her out. Then I would try and give him something else to play with to occupy his energy, like a towel he can dig into. If he’s biting or being aggressive about the chasing, I would stop him. A little chasing is okay but hardcore chasing can sometimes lead to a bunny brawl. Which you don’t want to have to break up.
I also wouldn’t be too worried about his jealousy. My bonded buns have begun doing the same thing. They have NEVER liked to be picked up or to sit on your lap for more like 3 seconds. All of a sudden they see the new bun sitting nicely in our arms, and BOOM. I have three other bunnies on top of me all wanting to be held even though 2 weeks ago they would’ve clawed off our faces just for trying to hold them! LOL.