Weeeeeeeell, failing lockpicking, first attempts at violence are gonna be class hunter style shoulder vs door maneuvers.

Failing that: is there an office of some sort in the boarding house, or like a... supply area a custodian would have used, a basement? She'll look for tools either from the boarding house or from the Anders house she's left, anything heavy and hefty enough to attempt to smash the lock or break the door itself - from wrenches to axes to firepokers to crowbars to just heavy pieces of furniture.

If all other attempts fail, Claire's going to spend a day searching the boarding house and her own + unclaimed rooms for maybe a key.

Or a flamethrower, which is potentially unrelated to the door, because she doesn't want to burn the house down yet.