In bridge-contract player 1 wins hand with dummy and claims the trick before playing her card. This was discovered at the end of the hand. What is the proper way to handle this?
I presume from your description that this incident is from a Rubber Bridge game (as opposed to a Duplicate or Tournament game). In this case the Laws of Rubber Bridge - 2017 apply; specifically Law 67 B:
Law 67 – Trick Either Appropriated in Error or Defective
A trick containing more or fewer than four cards is defective. When one player is found, during play, to have fewer or more cards than all of the other players, the previous tricks should be forthwith examined, face down; if a defective trick is discovered, the player with a correspondingly incorrect number of cards is held responsible. The defective trick is inspected face up and
B. after the responsible player has played to a subsequent trick,
the ownership of the defective trick cannot be changed and
if the offender has failed to play a card to the defective trick, he forthwith faces and adds a card to that trick, if possible one he could legally have played to it.
if the offender has played more than one card to the defective trick, [not applicable].
Note the three key points:
The offending player must add a card to the defective trick when it is discovered.
The card added must be one that could legally have been played to the trick.
The card added does not change the ownership of the trick.
This is different from the Laws of Contract Bridge - 1981 (personal copy), where the text reads:
(b) After all four hands have played to a subsequent trick,
(penalty) the defective trick, if won by the offending side, is transferred to the non-offending side;
and [the trick is corrected similarly to above]
I do not know in which year the change occurred in this rule.
If however you had been playing in a Tournament game then the Director should have been called immediately upon discovering the irregularity, with the stricter Law 67 B of the Laws of Duplicate Bridge - 2017 applying. Both because Duplicate players are expected to play in a more conscientious manner, and because irregularities affect the results of more than just the players at the table, penalties are often (and are in this case) stricter than in Rubber Bridge. The Revoke penalty applies in this case, with the offending player deemed to have revoked to the defective trick.