The most common and most likely answer to this crossword clue is the 5 letter word WORSE
I've seen this crossword clue in The Guardian
W
O
R
S
E
More clues leading to the result WORSE
- Eroded around front of ship — not so good
- Royal Society’s in misery with lower standards
- Poorer fretted outside society
- Inferior small bore going around
- Extremely restless in misery is not so good
- Not better with sore bum
- More bad language without a shred of decency – base!
- Sew around or it gets more difficult
- Inferior living in a bungalow or semi
- Swore to reform but hasn’t got any better
Buddy explains!

The straight part
We know that "Not better" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not better = worse.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 WORSE mean?
WORSE adjective- Unfavorable; negative; not good.
- Not suitable or fitting.
- Not appropriate, of manners etc.
- Unhealthy; liable to cause health problems.
- Sickly, unhealthy, unwell.
- Not behaving; behaving badly; misbehaving; mischievous or disobedient.
- Tricky; stressful; unpleasant.
- Evil; wicked.
- Faulty; not functional.
- (of food) Spoiled, rotten, overripe.
- (of breath) Malodorous; foul.
- False; counterfeit; illegitimate.
- Unskilled; of limited ability; not good.
- Of poor physical appearance.
- Bold and daring.
- Good, superlative, excellent, cool.
- (of a need, want, or pain) Severe, urgent.
- Overly promiscuous, licentious.
- (of a draft/check) Not covered by funds on account.
- In a bad manner.
- Very much; to a great degree.
- Evil; wicked (of people).
- Morally reprehensible (of behaviour etc.); blameworthy.
- Indicative of unkind or malevolent intentions; harsh, cruel.
- Unpropitious, unkind, faulty, not up to reasonable standard.
- Unwell in terms of health or physical condition; sick.
- Having an urge to vomit.
- (hip-hop slang) Sublime, with the connotation of being so in a singularly creative way.
- Extremely bad (bad enough to make one ill). Generally used indirectly with to be.
- Unwise; not a good idea.
- Not well; imperfectly, badly; hardly.
- Loss; disadvantage; defeat.
- That which is worse; something less good.
- To make worse; to put at disadvantage; to discomfit.