Tear off, certain to cherish (8)
I believe the answer is:
treasure
'cherish' is the definition.
('treasure' can be a synonym of 'cherish')
'tear off certain' is the wordplay.
'off' is an anagram indicator.
'certain' becomes 'sure' ('sure' can be a synonym of 'certain').
'tear' is an anagram of 'trea'.
'trea'+'sure'='TREASURE'
'to' acts as a link.
(Other definitions for treasure that I've seen before include "much-loved person" , "Hoard of jewels and money" , "Value highly" , "Quantity of precious objects" , "A quantity of valuable objects" .)