How Jay Garrick (John Wesley Shipp) was worked into Wally West (Keiynan Lonsdale).
That ended when she broke up with him via a hologram message. Later, it was made clear Jesse Quick had moved on from her days with Team Flash, as she now had her own team of superheroes she preferred to work with on Earth-2. Though Jesse didn’t return, she was seemingly killed off in the Arrow season 8 premiere when Earth-2 was wiped out by the Crisis. Jesse was assumed to be among the casualties by Team Flash. A memorial featured in a season 7 episode formally recognized her as one of the show’s fallen heroes.
Though it makes sense that an alternate Earth character like Jesse wouldn’t exist on Earth-Prime, it’s worth noting the Arrowverse did find room for Earth-3’s Jay Garrick. For a long time, there was much discussion over how he would be brought back, especially since Jay is a doppelganger of Barry’s father. Henry Allen is dead, but Jay’s existence on Earth-Prime would mean they did co-exist earlier in the timeline. Though that does sound like a potential problem, The Flash overlooked the issues with it and simply made Jay the Flash of Earth-Prime’s Keystone City.
Similar to the situation with Jay, there are obstacles to Jesse being on Earth-Prime too. Her backstory just isn’t compatible. Her father, Harry Wells, lived on an Earth that’s no longer a part of the multiverse. Earth-Prime’s Harrison Wells is a totally different person, and there certainly couldn't have been two of them. However, the Arrowverse keeping Jay Garrick around despite the obvious problems with it means it could find a way to do the same thing with Violett Beane’s Jesse.
At this juncture, Barry (Grant Gustin) and all the others believe Jesse is gone for good, but in reality, The Flash can write her back in at any given moment. After all, Team Flash has no proof that she’s dead. It could be she was secretly reborn with the creation of the new multiverse, possibly as a daughter of Harrison Wells that they don’t know about yet. If a post-Crisis Jesse Quick were to ever get both her speed and original memories back, she could develop a presence in The Flash season 8. Thanks to the Crisis, the series would have an opportunity to add new layers to her character and make any changes that would suit the story.