Vulgar Yankee old boy found by mistake (7)
I believe the answer is:
yobbish
'vulgar' is the definition.
(both can mean rude)
'yankee old boy found by mistake' is the wordplay.
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'old boy' becomes 'ob' (abbreviation).
'found by' says to put letters next to each other.
'mistake' becomes 'bish' (I've seen this before).
'y'+'ob'+'bish'='YOBBISH'
(Other definitions for yobbish that I've seen before include "Like a rude and aggressive youth" , "characteristic of a lout" , "Like a lout" , "Ill-bred" , "far from refined" .)