The most common and most likely answer to this crossword clue is the 7 letter word CROWDED
I've seen this crossword clue in The Daily Telegraph
C
R
O
W
D
E
D
Buddy explains!

The straight part
We know that "cramped" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cramped = crowded.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 CROWDED mean?
CROWDED verb- To press forward; to advance by pushing.
- To press together or collect in numbers
- To press or drive together, especially into a small space; to cram.
- To fill by pressing or thronging together
- (often used with "out of" or "off") To push, to press, to shove.
- To approach another ship too closely when it has right of way.
- (of a square-rigged ship) To carry excessive sail in the hope of moving faster.
- To press by solicitation; to urge; to dun; hence, to treat discourteously or unreasonably.
- To play on a crowd; to fiddle.
- Containing too many of something; teeming.