Otherwise raced to form a painting style (3,4)
I believe the answer is:
art deco
'style' is the definition.
(decorative style)
'otherwise raced to' is the wordplay.
'otherwise' indicates an anagram.
'raced'+'to'='racedto'
'racedto' is an anagram of 'ART DECO'.
'form a painting' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
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 design popular in the 1920s and 1930s" , "Nineteen twenty's and thirties style" , "Style popular in the 1920s and '30s" , "1920s and 30s style of art and architecture" .)