Red coat designed in 1930s style (3,4)
I believe the answer is:
art deco
'1930s style' is the definition.
(I've seen this before)
'red coat designed' is the wordplay.
'designed' indicates anagramming the letters (designed with the letters).
'red'+'coat'='redcoat'
'redcoat' anagrammed gives 'ART DECO'.
'in' acts as a link.
(Other definitions for art deco that I've seen before include "Architecture/design movement of the 1920s and 30s" , "Highly geometric style" , "Style of design popular in the 1920s and 1930s" , "Early C 20 style" , "pre-war style" .)