Characters Are Portable; Their Furniture Is Not
Writers get attached to details that belong to the setting rather than the person — the job, the car, the phone, the war they fought in. Move the character and those break, and the instinct is to find a one-to-one replacement. The detective becomes an investigator for the crown. The car becomes a horse.
That approach produces a character wearing a translated costume. The better question is which parts were ever the character at all.
Separate Role from Function
"Detective" is a role. The function underneath might be needs to know things other people are hiding. The role does not survive a move to a fantasy setting; the function survives anything. It could become a priest who hears confession, a servant in a great house, a cartographer.
Do this for every defining trait and you will find most of them are functions dressed as roles.
Keep the Wound, Change the Cause
A character shaped by a failed case can be shaped by a failed hunt, a lost siege, a broken oath. The event is setting-bound. The mark it left is not, and the mark is what people recognise.
Ask What the New Setting Makes Impossible
The most interesting part of a move is what the character loses. A modern character in a pre-literate world loses records, evidence, the ability to check. Someone whose whole identity was built on being able to verify things now cannot.
That is not a problem to solve. That is the story the move gives you for free.
Do Not Import Their Reputation
Characters carry accumulated standing — people who owe them, people who fear them. In a new setting none of that exists, and rebuilding it is where a lot of good early scenes come from. Skipping it makes the character feel imposed on the world rather than in it.
Version Them Rather Than Overwrite Them
Keep the original intact and make the new setting a separate version. Writers who overwrite usually regret it, because the two versions answer different questions and you will want both.
Practically: separate profiles, clearly named. It also spares your roleplay partners the confusion of a character whose history changed since they last read it.