The most common and most likely answer to this crossword clue is the 4 letter word HATE
I've seen this crossword clue in The Guardian
H
A
T
E
More clues leading to the result HATE
- Henry swallowed strong emotion
- Loathe contributing to church at Easter
- Detest bowler, perhaps — and Essex opener!
- Dislike seen in clash at Edgbaston
- Drinking a Tango he can’t stand
- Resent some that escaped
- One’s taken by the dancing, not love
- Hostility from bowlerinitially
- Bowler maybe with athlete’s foot can’t stand
- Bowler, perhaps English, can’t stand
Buddy explains!

The straight part
We know that "not love" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not love = hate.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 HATE mean?
HATE noun- An object of hatred.
- Hatred.
- Negative feedback, abusive behaviour.
- To dislike intensely or greatly.
- To experience hatred.