Private penning article that's comparatively silly (6)
I believe the answer is:
inaner
'comparatively silly' is the definition.
(more inane or silly)
'private penning article' is the wordplay.
'private' becomes 'inner' (as in one's private or inner thoughts).
'penning' is an insertion indicator.
'article' becomes 'a' (the indefinite article in English).
'inner' placed around 'a' is 'INANER'.
'that's' is the link.
(Other definitions for inaner that I've seen before include "Rather silly" , "More vacuous" , "More stupid" , "What's relatively lemon-like" , "More empty" .)