More roguish end to country's Olympic sport (7)
I believe the answer is:
archery
'olympic sport' is the definition.
'more roguish end to country's' is the wordplay.
'more roguish' becomes 'archer'.
'end to' says to take the final letters.
The final letter of 'country' is 'y'.
'archer'+'y'='ARCHERY'
(Other definitions for archery that I've seen before include "Toxophily" , "Target sport - Olympic event in from 1900-08, in 1920 and since 1972" , "The sport of shooting arrows with a bow" , "Bow and arrow sport" , "Arrow-shooting" .)