The most common and most likely answer to this crossword clue is the 7 letter word WARBIRD
I've seen this crossword clue in The Times
W
A
R
B
I
R
D
Buddy explains!

The straight part
We know that "old military plane" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old military plane = warbird.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 WARBIRD mean?
WARBIRD noun- An aircraft formerly operated by the military, but now owned privately.
- Any aircraft decorated in military livery for display at airshows etc.