The most common and most likely answer to this crossword clue is the 7 letter word STINTED
I've seen this crossword clue in The Times
S
T
I
N
T
E
D
Buddy explains!

The straight part
We know that "Kept short" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kept short = stinted.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 STINTED mean?
STINTED verb- To stop (an action); cease, desist.
- To stop speaking or talking (of a subject).
- To be sparing or mean.
- To restrain within certain limits; to bound; to restrict to a scant allowance.
- To assign a certain task to (a person), upon the performance of which he/she is excused from further labour for that day or period; to stent.
- (of mares) To impregnate successfully; to get with foal.
- Constrained; restrained; confined.