Figure in great pain, not unknown following year-end (7)
I believe the answer is:
decagon
'figure' is the definition.
(type of geometrical figure)
'great pain not unknown following year-end' is the wordplay.
'great pain' becomes 'agony' (I've seen this before).
'not' is a deletion indicator.
'unknown' becomes 'y' (algebra).
'following' is a charade indicator (letters next to each other).
'year end' becomes 'dec' (I can't justify this - if you can you should believe this answer much more).
'agony' with 'y' taken out is 'agon'.
'agon' put after 'dec' is 'DECAGON'.
'in' is the link.
Can you help me to learn more?
(Other definitions for decagon that I've seen before include "Plane shape" , "10-sided figure" , "A polygon -- eg can-do (anag)" , "Ten-sided plane figure" , "Go, dance on geometric figure with ten sides" .)