Redcoat dancing in style (3,4)
I believe the answer is:
art deco
'style' is the definition.
(decorative style)
'redcoat dancing' is the wordplay.
'dancing' indicates anagramming the letters.
'redcoat' is an anagram of 'ART DECO'.
'in' is the link.
(Other definitions for art deco that I've seen before include "Redcoat (anag) -- inter-war design style" , "Nineteen twenty's and thirties style" , "1920s and 1930s ornamental style" , "nineteen thirty's style" , "Early C 20 style" .)