Silly cousin an embarrassment, partially (5)
I believe the answer is:
inane
'silly' is the definition.
(inane means silly or foolish)
'cousin an embarrassment partially' is the wordplay.
'partially' says the answer is hidden in the clue.
'INANE' is hidden in the letters of 'cousin an embarrassment'.
(Other definitions for inane that I've seen before include "Thick" , "Frivolous" , "Empty" , "Vapid, fatuous" , "Delirious" .)