Building style of party with Republican in charge (5)
I believe the answer is:
doric
'building style' is the definition.
(architectural style)
'party with republican in charge' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'with' says to put letters next to each other.
'republican' becomes 'r' (abbreviation).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'do'+'r'+'ic'='DORIC'
'of' acts as a link.
(Other definitions for doric that I've seen before include "Style of column" , "Type of column" , "hairdo tips costly, for the most part" , "Plainest order of Gk. architecture" , "Ancient dialect" .)