Continues to final Sunday (5)
I believe the answer is:
'continues' is the definition.
(I've seen this in another clue)
'final sunday' is the wordplay.
'final' becomes 'last' (synonyms).
'sunday' becomes 's'.
'to' is the link.
(Other definitions for lasts that I've seen before include "Holds out" , "carries on" , "Goes on" , "Endures" , "Cobblers' tools" .)