Shallow and largely fake — bigly! (4)
I believe the answer is:
glib
'shallow' is the definition.
('glib' can be a synonym of 'shallow')
I cannot understand how the rest of the clue works.
(Other definitions for glib that I've seen before include "smooth" , "Superficially facile with words" , "slick in speech" , "Having only superficial plausibility" , "Bush" .)