An article on bustle.com has some theories. It is quoted below.
As far as the show is concerned, Kristen Kringle works with Edward Nygma (who will eventually become the Riddler, E-Nygma, crafty isn't it?) at the Gotham City Police Department as an archivist, and the latter seems to have developed some romantic feelings towards her. As the article on bustle.com points out
Though Kristen has acted solely as a love interest for Edward so far, the Gotham writers must have something more in store for her.
- She’ll be Turning Into Harley Quinn
The Hollywood Reporter suggested the possibility of Kris turning into Harley Quinn, a character who debuted in the Batman comics as a female sidekick to the Joker.
But this may necessarily not be the case here, as she is introduced as a counterpart (so far) of Riddler in the show and not Joker, and Joker has not even made an entry in Gotham so far.
- She’s Santa Claus’ Daughter
Well, we have seen Santa share the page with the Dark Knight before (kind of) and he wasn’t
the jolly old soul he’s portrayed to be in popular culture. Instead, he had an army of elves and was decapitated by intergalactic bounty hunter Lobo. Observer suggests that Kris could be Santa's daughter.
- She’s Related To Mr. Freeze
Now this is a rather long shot. It's
along the same lines as the Santa Claus theory, because Kringle = Santa = North Pole = Mr. Freeze.
But then again, these are as much as we can come up with at this point of time.