Most slimy East German admits: 'You can't believe me' (7)
I believe the answer is:
oiliest
'most slimy' is the definition.
'east german admits you can't believe me' is the wordplay.
'east german' becomes 'ost' ('east' in the german language).
'admits' means one lot of letters goes inside another.
'you can't believe me' becomes 'i lie'.
'ost' enclosing 'ilie' is 'OILIEST'.
(Other definitions for oiliest that I've seen before include "Most unctuous" , "Most greasy" , "Most flattering" .)