Permanence of ill repute — shame about that (10)
I believe the answer is:
perpetuity
'permanence' is the definition.
(perpetuity is a kind of permanence)
'ill repute shame about that' is the wordplay.
'ill' indicates anagramming the letters.
'shame' becomes 'pity' ('pity' can be a synonym of 'shame').
'about that' means one lot of letters goes inside another.
'repute' anagrammed gives 'erpetu'.
'erpetu' going within 'pity' is 'PERPETUITY'.
'of' acts as a link.
(Other definitions for perpetuity that I've seen before include "In(de)finite duration" , "In this is forever" .)