Accepted a second problem with eastern diamonds (7)
I believe the answer is:
assumed
'accepted' is the definition.
('assume' can be a synonym of 'accept')
'a second problem with eastern diamonds' is the wordplay.
'second' becomes 's' (common abbreviation).
'problem' becomes 'sum' (arithmetic problem).
'with' means one lot of letters go next to another.
'eastern' becomes 'e'.
'diamonds' becomes 'd' (abbreviation for the card suit diamonds).
'a'+'s'+'sum'+'e'+'d'='ASSUMED'
(Other definitions for assumed that I've seen before include "Surmised" , "Accepted as true without actual proof" , "Taken as true; adopted" , "Seized" , "Put it on - without being told?" .)