The most common and most likely answer to this crossword clue is the 6 plus 9 letter word LITTLE ENGLANDER
I've seen this crossword clue in Financial Times
L
I
T
T
L
E
E
N
G
L
A
N
D
E
R
Buddy explains!
The straight part
We know that "He’s desperate to get out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case he’s desperate to get out = little englander.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.