The most common and most likely answer to this crossword clue is the 7 letter word DUNKIRK
I've seen this crossword clue in Financial Times
D
U
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K
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K
More clues leading to the result DUNKIRK
- Kind of indefatigable spirit appearing in a grey-brown church
- Dingy church in French port
- Dip one’s biccy — to be annoying — in port
- Dingy church has a place in modern history
- Dingy Scottish church from where host was rescued
- Withdrawal of bug firstly put in hot liquid
- Pester captain boldly going to effect military evacuation
Buddy explains!

The straight part
We know that "Kind of indefatigable spirit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kind of indefatigable spirit = dunkirk.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.