Guaranteed right to enter petition in extremity (7)
I believe the answer is:
ensured
'guaranteed' is the definition.
('ensure' can be a synonym of 'guarantee')
'right to enter petition in extremity' is the wordplay.
'right' becomes 'r' (abbreviation).
'to enter' indicates putting letters inside.
'petition' becomes 'sue' (both can mean to appeal or ask for something).
'in' is an insertion indicator.
'extremity' becomes 'end' (end is a kind of extremity).
'r' placed within 'sue' is 'sure'.
'sure' going inside 'end' is 'ENSURED'.
(Other definitions for ensured that I've seen before include "Made certain for end user" , "guaranteed" , "Make certain of" , "Saw to it" , "Determined" .)