The most common and most likely answer to this crossword clue is the 1 plus 3 plus 2 plus 3 plus 4 letter word A BIT ON THE SIDE
I've seen this crossword clue in Financial Times
A
B
I
T
O
N
T
H
E
S
I
D
E
More clues leading to the result A BIT ON THE SIDE
- Shaking hesitation, bed one's mistress
- Mistress, maybe, with item of gossip about team?
- An affair with a lover that’s somewhat edgy
- Paramour slightly off-centre?
- Source of illicit fun — some here?
- Relationship that might make you somewhat on edge?
- Active antibodies, the secret of a cheat?
- The antibodies destroyed illicit lover
- Continue having sex with hot steno slyly in an extramarital relationship
- Lover from America nibbled flank?
Buddy explains!

The straight part
We know that "Lover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lover = a bit on the side.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.