The most common and most likely answer to this crossword clue is the 4 letter word EXES
I've seen this crossword clue in The Guardian
E
X
E
S
More clues leading to the result EXES
- Upset some oversexed old lovers
- Get upset about unknown people no longer with us
- Kisses for old lovers
- Old lovers need tablet – nooky when erect?
- Costs incurred and claimed by people once married?
- Charms eroded initially for old lovers
- Old lovers — they may be associated with financial claims
- Former partners and former opponents at bridge
- What could be money for employees entertaining has-beens
- Claims made by former union members
Buddy explains!

The straight part
We know that "Kisses/old lovers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kisses/old lovers = exes.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.
What does EXES mean?
EXES noun- The name of the Latin-script letter X.
- A former partner or spouse, usually short for ex-girlfriend, ex-boyfriend, ex-wife or ex-husband.
- To delete; to cross out
- (costers) The number six.
- (betting) Odds of six to one.