Encounter to be satisfactory regarding ancient sport (10)
I believe the answer is:
battledore
'ancient sport' is the definition.
'battledore' can be an answer for 'sport' (battledore is a kind of sport). I'm not certain of the 'ancient' bit.
'encounter to be satisfactory regarding' is the wordplay.
'encounter' becomes 'battle' (I've seen this before).
'to be satisfactory' becomes 'do' (I am not sure about this - if you are sure you should believe this answer much more).
'regarding' becomes 're' (re can mean regarding, concerning).
'battle'+'do'+'re'='BATTLEDORE'
Can you help me to learn more?
(Other definitions for battledore that I've seen before include "Forerunner of Badminton" , "game" , "Not much of a racket" .)