Skinhead cheers Republican VIP (4)
I believe the answer is:
star
'vip' is the definition.
(both can mean an important or famous person)
'skinhead cheers republican' is the wordplay.
'skinhead' becomes 's' (head letter of 'skin').
'cheers' becomes 'ta' (both can mean thank you).
'republican' becomes 'R' (abbreviation in US politics).
's'+'ta'+'r'='STAR'
(Other definitions for star that I've seen before include "Celestial body of hot gases" , "Top celebrity" , "Top performer" , "Celebrated performer" , "See 21" .)