Minor player's age? About ten at the start (5)
I believe the answer is:
extra
'minor player's' is the definition.
'extra' can be an answer for 'player's' (extra is a kind of player). I'm not sure about the 'minor' bit.
'age? about ten at the start' is the wordplay.
'age?' becomes 'era' (both can mean a long time).
'about' indicates putting letters inside.
'ten' becomes 'X' (Roman numeral).
'at the start' becomes 't' (I can't justify this - if you can you should believe this answer much more).
'x'+'t'='xt'
'era' going around 'xt' is 'EXTRA'.
Can you help me to learn more?
(Other definitions for extra that I've seen before include "Left over" , "more than usually" , "Actor's part" , "Actor in non-speaking role" , "Additional or supplementary" .)