Astonished at the publicity about a puzzle (6)
I believe the answer is:
amazed
'astonished' is the definition.
(synonyms)
'the publicity about a puzzle' is the wordplay.
'the publicity' becomes 'ad' (short for advertisement).
'about' is an insertion indicator.
'a puzzle' becomes 'maze' (maze can mean a puzzling situation).
'ad' going around 'maze' is 'AMAZED'.
'at' acts as a link.
(Other definitions for amazed that I've seen before include "was stunning" , "Astonished, stunned" , "Staggered" , "Astonished, astounded" , "Overwhelmed with wonder" .)