Supporter of PM once getting mouthful over lie (8)
I believe the answer is:
blairite
'supporter of pm once' is the definition.
(supporter of Tony Blair)
'mouthful over lie' is the wordplay.
'mouthful' becomes 'bite' (a bite of food).
'over' is an insertion indicator.
'lie' becomes 'lair' (lie can mean an animal's lair).
'bite' enclosing 'lair' is 'BLAIRITE'.
'getting' is the link.
(Other definitions for blairite that I've seen before include "Of Labour's reforming policies" , "Tony's crony?" , "Bluey-red" .)