In America, a slight girl coming out clutching the Guardian (5)
I believe the answer is:
dweeb
'in america a slight' is the definition.
(American insult or slight)
'girl coming out clutching the guardian' is the wordplay.
'girl coming out' becomes 'deb' (short for debutante).
'clutching' is an insertion indicator.
'the guardian' becomes 'we' (the crossword setter and their Guardian colleagues).
'deb' enclosing 'we' is 'DWEEB'.
(Other definitions for dweeb that I've seen before include "Antisocial guy" , "Fool" , "(US) idiot" , "Nerd - wimp" , "Boringly studious student" .)