Compete with conviction (4)
I believe the answer is:
view
'conviction' is the definition.
(I've seen this before)
'compete with' is the wordplay.
'compete' becomes 'vie' (synonyms).
'with' becomes 'w' (abbreviation).
'vie'+'w'='VIEW'
(Other definitions for view that I've seen before include "Aspect, scene" , "judgment" , "Consider" , "general survey" , "Sight - opinion" .)