Decent time obtained in pursuit (6)
I believe the answer is:
chaste
'decent' is the definition.
(both can mean modest or proper)
'time obtained in pursuit' is the wordplay.
'time' becomes 't' (abbreviation).
'obtained in' means one lot of letters goes inside another.
'pursuit' becomes 'chase' (synonyms).
't' going into 'chase' is 'CHASTE'.
(Other definitions for chaste that I've seen before include "'Celibate, virginal (6)'" , "Refraining from sex" , "Everlasting" , "Modest and decent" , "Pure and virginal" .)