Toothless old PM associated with gallery (8)
I believe the answer is:
edentate
'toothless' is the definition.
(edentate means lacking teeth)
'old pm associated with gallery' is the wordplay.
'old pm' becomes 'eden' (Anthony Eden, UK prime minister 1955-1957).
'associated with' means one lot of letters go next to another.
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'eden'+'tate'='EDENTATE'
(Other definitions for edentate that I've seen before include "sloth, say" , "Toothless creature" , "Toothless mammal" , "lacking bite" , "Gummy" .)