American, in private, is sillier (6)
I believe the answer is:
inaner
'sillier' is the definition.
(I've seen this in another clue)
'american in private' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' indicates putting letters inside.
'private' becomes 'inner' (as in one's private or inner thoughts).
'a' going into 'inner' is 'INANER'.
'is' is the link.
(Other definitions for inaner that I've seen before include "More stupid" , "What's relatively lemon-like" , "Rather silly" , "More empty" , "More vacuous" .)