The most common and most likely answer to this crossword clue is the 10 letter word KENNELLING
K
E
N
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L
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Buddy explains!
The straight part
We know that "being cooped up like a pet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case being cooped up like a pet = kennelling.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 KENNELLING mean?
KENNELLING verb- To house or board a dog (or less commonly another animal).
- To lie or lodge; to dwell, as a dog or a fox.
- To drive (a fox) to covert in its hole.