A cup to suffer degeneration (7)

I believe the answer is:

atrophy

I'm a little stuck... Click here to teach me more about this clue!

'degeneration' is the definition.
(I've seen this before)

'a cup' is the wordplay.
'cup' becomes 'trophy' (I've seen this before).
'a'+'trophy'='ATROPHY'

'to suffer' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for atrophy that I've seen before include "Decay" , "wasting away" , "Waste away as through lack of food" , "Waste away (from disuse?)" , "Degenerate" .)

I've seen this clue in the Sydney Morning Herald.

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