Sloth maybe of Etonian PM, say, losing face (8)
I believe the answer is:
edentate
'sloth maybe' is the definition.
(sloth is an example of an edentate animal)
'etonian pm say losing face' is the wordplay.
'etonian pm' becomes 'eden' (former prime minister Anthony Eden. I am not sure about the 'etonian' bit.).
'say' becomes 'state' (synonyms).
'losing face' means to remove the first letter.
'state' with its first letter taken away is 'tate'.
'eden'+'tate'='EDENTATE'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for edentate that I've seen before include "anteater for one" , "lacking bite" , "Gummy" , "sloth, say" , "sloth, for example" .)