Apply oneself in serious contest (3-2)
I believe the answer is:
set-to
I believe this is a double definition.
'apply oneself' is the first definition.
(as in setting oneself to a task)
'serious contest' is the second definition.
(a set-to is a confrontation or disagreement)
'in' acts as a link.
(Other definitions for set-to that I've seen before include "Brief fight" , "Ready - fight" , "brush with violence?" , "Altercation" , "Fight, argument" .)