Adulates with unseemly oiliness (8)
I believe the answer is:
lionises
'adulates' is the definition.
(to lionise is to worship or celebrate)
'unseemly oiliness' is the wordplay.
'unseemly' indicates anagramming the letters.
'oiliness' anagrammed gives 'LIONISES'.
'with' is the link.
(Other definitions for lionises that I've seen before include "Treats as celebrity" , "Assigns great social importance to" .)