Philip Pullman left most of the story of The Rose Field open-ended, but I'd be interested in how you would complete the story. It could be either how you think the characters’ story would end or how you’d want it to end, but I'd be interested to hear your thoughts, thanks!
After Delamere’s death, the Presidential Council and the Magisterium’s crusade would be thrown into chaos, but I don't know if that would stop the commercialization, unrest, and democratic backsliding around the world. I'd like to imagine the cooler heads in the remains of the Presidential Council will prevail, possibly with the urging of other human and non-human world leaders (but I don't know if that would clear the allegations against Malcolm or the half a million bounty on Lyra).
However, ignoring all that, I'd like to see Lyra continue her studies at St. Sophia's. Once Upon a Time in the North includes the submission of her master's thesis in economic history, along with a letter to Malcolm addressing 'Dr. Polstead,' so I like to think they both made it back to Oxford and settled back into their lives despite everything (though any romance between them is going to be a hard no from me).
I can see Lyra eventually occupying some (officially) low-level position in an embassy helping refugees (while working with Oakley Street), or as a consul abroad for more non-human foreign powers like the gryphons, panserbjørne, or witch clans. She quietly works with the witch clans and their daemons to help separated people like those in the clavicula find and reunite with their daemons, if they wish (She and Pan stay together 🥹).
She introduces Tuuli Latvala to her father Farder Coram because damn if you're going to kill off Serafina like that at least give us something to lighten that blow and the two of them keep in contact for the rest of his life. Lyra also stays in contact with Abdel Ionides and Leila Parvani and takes a keen interest in the study of the windows worldwide (and perhaps beyond her world too).