Barbarian in charge of architectural style (6)
I believe the answer is:
gothic
'architectural style' is the definition.
(Gothic is an example)
'barbarian in charge' is the wordplay.
'barbarian' becomes 'goth' ('Goth' can be a synonym of 'barbarian').
'in charge' becomes 'ic'.
'goth'+'ic'='GOTHIC'
'of' acts as a link.
(Other definitions for gothic that I've seen before include "Building style of medieval cathedrals" , "horrifying" , "Style of architecture, literatureand film" , "Style of mediaeval architecture" , "Style of architecture with high pointed arches" .)