Treasures former PM's wife's keeping shut up (9)
I believe the answer is:
cherishes
'treasures' is the definition.
('cherish' can be a synonym of 'treasure')
'former pm's wife's keeping shut up' is the wordplay.
'former pm's wife's' becomes 'Cherie's' (Cherie Blair, wife of Tony Blair).
'keeping' indicates putting letters inside.
'shut up' becomes 'sh'.
'cheries' going around 'sh' is 'CHERISHES'.
(Other definitions for cherishes that I've seen before include "Is fond of, keeps in one's heart" , "Loves" .)