First of all, great job identifying the problem. Possessiveness sounds spot on to me.
Most importantly, never ever use any kind of punishment (physical corrections, slapping, pushing, pinning to the ground, leash jerks, etc.) to try to correct this kind of behavior. It is highly ineffective and actually exacerbates the problem because the pup will associate the punishment with the presence of the other dog. I only mention this because I see and hear this a lot and these techniques are still being taught in some dog training programs and online resources, so beware!
What I would suggest is use positive reinforcement training to teach the new pup to enjoy when other dogs are close to you. You do this by making sure she is doing something she loves or getting something she loves whenever other dogs are near you or you are petting other dogs. This can be accomplished in a number of ways like giving her treats whenever another new dog comes in view, providing her favorite toy to chew on, playing fetch with her, giving her an interactive treat-dispensing toy, feeding her meals when you are giving another dog attention, etc. You can also give both dogs affection at the same time if she can tolerate this without becoming aggressive. If she can do this without issue, then progress to taking short breaks from petting her while you're still petting the other dog (1-2 seconds at first, then increasing very slowly).
This one may or may not apply to you, but another thing you can try is giving her less attention in general, depending on what she's usually like around you. If she often comes up to nudge you for pets or jumps on you when you enter the room, it would probably help to ignore her (no eye contact, no physical contact) until she calms down. This will help train her to be a little more independent and self-soothing.
Pay attention to your own emotional state. If you feel nervous, stressed, tense, frustrated, angry, etc. (which would be understandable given what's happening!), work on being calm, confident, and assertive. Also, talking in these situations can often make it worse or trigger a confrontation, so try to communicate more with your body language or use your voice only to encourage good behavior when your pup is relaxed and doing well.
And of course, you can always hire a professional dog trainer who uses positive reinforcement.
I recently read this article by Whole Dog Journal on curbing dog aggression, and I love it.
https://www.whole-dog-journal.com/iss...12/features/Teaching-an-Aggressive-Dog-to-Socialize5417-1.html
Hope this helps. Good luck!