The most common and most likely answer to this crossword clue is the 5 letter word EJECT
I've seen this crossword clue in The Guardian
E
J
E
C
T
More clues leading to the result EJECT
- European clubs wearing black kick out
- Turf out a hundred boarding European plane
- Remove European plane holding 100
- Turn out for Louis I in European court
- Throw out English judge before European court
- Bale out from European plane, leaving a hundred inside
- What pilot may do, caught in European plane
- Throw out film about Japanese city
- Chuck out defective item with missing lid
- Dismiss European high-flier that’s taken cocaine
Buddy explains!

The straight part
We know that "exile" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exile = eject.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 EJECT mean?
EJECT verb- To compel (a person or persons) to leave.
- To throw out or remove forcefully.
- To compel (a sports player) to leave the field because of inappropriate behaviour.
- To project oneself from an aircraft.
- To cause (something) to come out of a machine.
- To come out of a machine.
- An inferred object of someone else's consciousness