Last to finish cure, getting rid of cold (6)
'last' is the definition.
('endure' can be a synonym of 'last')
'finish cure getting rid of cold' is the wordplay.
'finish' becomes 'end' ('end' can be a synonym of 'finish'**).
'getting rid of' is a deletion indicator.
'cold' becomes 'c' (eg on taps).
'cure' with 'c' removed is 'ure'.
'to' is the link.
(Other definitions for endure that I've seen before include "Bear something patiently", "Stand", "Suffer, tolerate", "Undergo hardship patiently", "'Last, bear (6)'".)