Greek character on time, he volunteers (5)
I believe the answer is:
theta
'greek character' is the definition.
(letter from the Greek alphabet)
'on time he volunteers' is the wordplay.
'on' says to put letters next to each other.
'time' becomes 't'.
'volunteers' becomes 'ta' (abbreviation for Territorial Army).
't' next to 'he' is 'the'.
'the'+'ta'='THETA'
(Other definitions for theta that I've seen before include "Greek letter equivalent to th" , "letter from Athens" , "classic character?" , "Greek letter used in trigonometry" , "letter from abroad" .)