Mature writer is after religious instruction (5)
I believe the answer is:
ripen
'mature' is the definition.
(to ripen is to mature)
'writer is after religious instruction' is the wordplay.
'writer' becomes 'pen' (something which writes).
'is after' says to put letters next to each other.
'religious instruction' becomes 'RI' (abbreviation).
'pen' put after 'ri' is 'RIPEN'.
(Other definitions for ripen that I've seen before include "Become ready to eat" , "come near to falling" , "Become ready for picking" , "Grow to maturity like fruit" , "Mature, develop" .)