Style in embroidery of red coat (3,4)
I believe the answer is:
art deco
'style in embroidery' is the definition.
'art deco' can be an answer for 'style' (decorative style). I am not sure about the 'in embroidery' bit.
'of red coat' is the wordplay.
'of' indicates anagramming the letters (the answer comes from or 'of' the letters).
'red'+'coat'='redcoat'
'redcoat' with letters rearranged gives 'ART DECO'.
Can you help me to learn more?
(Other definitions for art deco that I've seen before include "1920s and 1930s style of ornamentation" , "Style of decorative art popular in 1920s and 1930s" , "Aesthetic style" , "Architecture/design movement of the 1920s and 30s" , "1920s and 30s style of art and architecture" .)