So to give some context, Serie is Frieren's teacher's teacher. Frieren herself has a bit of a side quest going on where she wants to learn as much magic as possible, and Serie indulges that as and when she feels like it. I can only really guess, but I would imagine she'd have some positive interaction by targeting Frieren. Flamme (York's claim) maybe less so, Flamme is Frieren's teacher and Serie's apprentice (also dead before the series starts).
The general idea is Frieren is essentially a long-lifed species. She joined a party of heroes to slay the Demon King (classic Fantasy setup), the party succeeded and that was that. To Frieren, it was very much "this journey is just a means to an end". However, this wasn't the case for her party - for them, who live shorter lives, it was their great work whereas it was basically like a blink for Frieren with her life span. It's also strongly suggested that the main hero of the party, Himmel, had feelings for Frieren but left them unsaid as they appeared to be unrequited. Over time, Frieren realises that she missed the joy of the journey and didn't truly appreciate what they'd done, but of course it's too late now. Himmel is dead, the rest of her party are very old and past their adventuring days if not dying themselves. And Frieren wants nothing more than to say what she couldn't back when they were in their prime, so she's looking for a spell to communicate with the dead. Basically she doesn't want to accept her regrets and laments not understanding humans better like she does now.
Serie is much older than Frieren and generally finds her amusing so isn't really antagonistic, though Frieren doesn't like her much. To be perfectly honest I think Serie fits very well as a Jack of All Trades type but I can see the angle for being cop. Would say outside of Frieren the only ones she would really likely have an interaction with (maybe Flamme but I'm not really compelled on that as they're not particularly close) would be Ubell and Fern.