Slick and regularly social yankee (4)
I believe the answer is:
oily
'slick' is the definition.
(I've seen this in another clue)
'regularly social yankee' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
The alternating letters of 'social' are 'oil'.
'oil'+'y'='OILY'
'and' acts as a link.
(Other definitions for oily that I've seen before include "Oleaginous" , "Covered in lubricant" , "Viscous" , "Smarmy" , "Smooth; like lubricant" .)