The most common and most likely answer to this crossword clue is the 3 plus 4 letter word OLD MAID
I've seen this crossword clue in The Times
O
L
D
M
A
I
D
More clues leading to the result OLD MAID
Buddy explains!
The straight part
We know that "Game of cards/one's left on the shelf" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case game of cards/one's left on the shelf = old maid.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.