The most common and most likely answer to this crossword clue is the 12 letter word RAGGEDÂ STAFF
I've seen this crossword clue in The Guardian
R
A
G
G
E
D
Â
S
T
A
F
F
Buddy explains!
The straight part
We know that "a contribution to Warwickshire’s coat of arms" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a contribution to warwickshire’s coat of arms = ragged staff.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.