They suffer damage years after contract's termination (7)
I believe the answer is:
martyrs
'they suffer' is the definition.
(a martyr is made to suffer)
'damage years after contract's termination' is the wordplay.
'damage' becomes 'mar' (to mar is to spoil or damage).
'years' becomes 'yrs' ('yr' can be a synonym of 'year').
'after' means one lot of letters go next to another.
'termination' indicates one should take the final letters.
The last letter of 'contract' is 't'.
'yrs' put after 't' is 'tyrs'.
'mar'+'tyrs'='MARTYRS'
(Other definitions for martyrs that I've seen before include "People who die for their cause" , "Persons suffering for their beliefs" , "They suffer for a principle" , "Those dying for their belief" , "people who suffer" .)