The most common and most likely answer to this crossword clue is the 6 letter word NEATER
N
E
A
T
E
R
Buddy explains!

The straight part
We know that "Better put" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case better put = neater.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 NEATER mean?
NEATER adjective- Clean, tidy; free from dirt or impurities.
- Free from contaminants; unadulterated, undiluted. Particularly of liquor and cocktails; see usage below.
- Conditions with a liquid reagent or gas performed with no standard solvent or cosolvent.
- With all deductions or allowances made; net.
- Having a simple elegance or style; clean, trim, tidy, tasteful.
- Well-executed or delivered; clever, skillful, precise.
- Facile; missing complexity or details in the favor of convenience or simplicity.
- Good, excellent, desirable.