Toothless Prime Minister introducing art gallery (8)
I believe the answer is:
edentate
'toothless' is the definition.
(edentate means lacking teeth)
'prime minister introducing art gallery' is the wordplay.
'prime minister' becomes 'eden' (I've seen this before).
'introducing' means one lot of letters go next to another (some letters go before others).
'art gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'eden'+'tate'='EDENTATE'
(Other definitions for edentate that I've seen before include "Toothless creature" , "Mammal with few or no teeth" , "sloth, for example" , "Gummy" , "Toothless mammal" .)