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