Old boy, essentially impertinent and vulgar, gets stick out (7)
I believe the answer is:
obtrude
'stick out' is the definition.
(I've seen this in another clue)
'old boy essentially impertinent and vulgar' is the wordplay.
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'essentially' says to take the centre.
'and' says to put letters next to each other.
'vulgar' becomes 'rude' (vulgar can mean rude or gross).
The middle letter of 'impertinent' is 't'.
'ob'+'t'+'rude'='OBTRUDE'
'gets' is the link.
(Other definitions for obtrude that I've seen before include "Be offensively prominent" , "Doubter (anag)" , "Push oneself in an unwelcome way" , "Become unwelcomely prominent" , "Barge in" .)