Note in Rule Ten wrong about competition at court (4,6)
I believe the answer is:
lawn tennis
'competition at court' is the definition.
(competition on a tennis court)
'note in rule ten wrong' is the wordplay.
'note' becomes 'n' (abbreviation).
'in' indicates putting letters inside.
'rule' becomes 'law' (law is a kind of rule).
'ten wrong' becomes 'tennis' (I can't justify this - if you can you should believe this answer much more).
'law'+'tennis'='lawtennis'
'n' going inside 'lawtennis' is 'LAWN TENNIS'.
'about' acts as a link.
(Other definitions for lawn tennis that I've seen before include "sport" , "court action results" , "Wimbledon game" , "Court game" , "Real alternative" .)