Close to Oamaru, back in New Zealand, ice finally melted (7)
I believe the answer is:
unfroze
'melted' is the definition.
('unfreeze' can be a synonym of 'melt')
'close to oamaru back in new zealand ice finally' is the wordplay.
'close to' suggests the final letters (the close/ending of).
'back' becomes 'fro' ('fro' can be a synonym of 'back'**).
'in' indicates putting letters inside.
'new zealand' becomes 'nz'.
'finally' says to take the final letters.
The last letter of 'oamaru' is 'u'.
The final letter of 'ice' is 'e'.
'fro' going within 'nz' is 'nfroz'.
'u'+'nfroz'+'e'='UNFROZE'
(Other definitions for unfroze that I've seen before include "melted" , "Relaxed restrictions!" .)