The most common and most likely answer to this crossword clue is the 6 letter word STRIVE
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The straight part
We know that "endeavour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case endeavour = strive.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 STRIVE mean?
STRIVE noun- Striving; earnest endeavor; hard work.
- Exertion or contention for superiority, either by physical or intellectual means.
- Bitter conflict, sometimes violent.
- A trouble of any kind.
- That which is contended against; occasion of contest.