Mischievous English rector with yen for sport (7)
I believe the answer is:
archery
'for sport' is the definition.
(archery is a kind of sport)
'mischievous english rector with yen' is the wordplay.
'mischievous' becomes 'arch' (arch can mean mischievous or playful).
'english' becomes 'E' (abbreviation).
'rector' becomes 'r'.
'with' is a charade indicator (letters next to each other).
'yen' becomes 'y' (resembles the symbol for the currency of Japan).
'arch'+'e'+'r'+'y'='ARCHERY'
(Other definitions for archery that I've seen before include "Bow and arrow sport" , "Bowman's sport" , "The sport of bowmen" , "Target sport - Olympic event in from 1900-08, in 1920 and since 1972" , "The sport of shooting arrows with a bow" .)