What is the penalty if the opposing team inadvertently plays two cards on a trick because they stick together. It is discovered later.
Assuming you are playing rubber bridge, the Laws of Rubber Bridge apply.
If the irregularity is discovered part way through the hand, was a misplay by a Defender, and during discovery of the misplayed card it was ever placed such that Offender's Partner could have seen the card then it becomes an exposed card subject to the Penalty Card rules.
Additionally, if the irregularity is discovered any time before the play is complete and the cards collected for shuffling, then the possibility of a revoke must be checked whether Offender was Declarer or a Defender. The card played in error must be regarded as being in the Offender's hand continuously from the trick of the misplay until noticed and restored. This can result in a revoke for the misplayed card. The applicable rule is:
Law 67 - Trick Either Appropriate 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 played more than one card to the defective trick, he withdraws all but one card, leaving the highest card he could legally have played to that trick. A withdrawn card may become a penalty card (Law 50); such a card is deemed to have belonged continuously to the offender’s hand and failure to have played it to an earlier trick may constitute a revoke.
This is basically an "exposed card" issue (assuming it was clear which card was intended to be played, as it must have been to have only been "discovered later").
And if the card being "lost" (stuck) causes another misplay before it is found (a revoke, for example), then that misplay will also have to be handled, of course. The misplay does not grant immunity to the other rules.
If the exposed (stuck) card was played by the declarer, no penalty (the declarer is not restricted).
If the exposed card was played by a defender and the partner could see its face, then it is subject to Law 49 and becomes a penalty. It remains exposed in front of its player until rectification (Law 50).
If it's below the rank of an honor, it's a minor penalty card. If it's an honor card, it's a major penalty card.
Minor: the player may not play any other card of the same suit below the rank of an honor until he has first played the penalty card, but he is entitled to play an honor card instead.
Major: A major penalty card must be played at the first legal opportunity, whether in leading, following suit, discarding or trumping. If the player's partner is to lead, then the declarer chooses whether the partner must lead the penalty card's suit or if he is to be prohibited from doing so.
Note: links are to duplicate bridge laws, but the same laws (and same numbers) apply for rubber bridge, as @ForgetIWasEverHere notes: https://cdn.acbl.org/wp-content/uploads/2015/02/Laws-of-Rubber-Bridge.pdf