The most common and most likely answer to this crossword clue is the 7 letter word GLOATED
I've seen this crossword clue in The Times
G
L
O
A
T
E
D
More clues leading to the result GLOATED
Buddy explains!

The straight part
We know that "Crew" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case crew = gloated.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 GLOATED mean?
GLOATED verb- To exhibit a conspicuous (sometimes malevolent) pleasure or sense of self-satisfaction, often at an adversary's misfortune.
- To triumph, crow, relish, glory, revel.