The most common and most likely answer to this crossword clue is the 9 letter word EXECUTION
I've seen this crossword clue in The Guardian
E
X
E
C
U
T
I
O
N
Buddy explains!
The straight part
We know that "A kind of exit on cue" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a kind of exit on cue = execution.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 EXECUTION mean?
EXECUTION noun- The act, manner or style of executing (actions, maneuvers, performances).
- The state of being accomplished.
- The act of putting to death or being put to death as a penalty, or actions so associated.
- The carrying into effect of a court judgment, or of a will.
- The formal process by which a contract is made valid and put into binding effect.
- The carrying out of an instruction, program or program segment by a computer.