Refused, last month, to have inner layer added (8)
I believe the answer is:
declined
'refused' is the definition.
('decline' can be a synonym of 'refuse')
'last month to have inner layer added' is the wordplay.
I cannot really understand how this works, but
'month' could be 'dec' (abbreviation for December) and 'dec' is located in the answer.
The remaining letters 'lined' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for declined that I've seen before include "Turned down < , fell off" , "Went through cases" , "Refused; waned" , "Refused or weakened" , "Said no, refused" .)