Upset about limits to dud puzzle (6)
I believe the answer is:
riddle
'puzzle' is the definition.
(a riddle is a puzzle or problem)
'upset about limits to dud' is the wordplay.
'upset' becomes 'rile' (to rile is to annoy or upset).
'about' means one lot of letters goes inside another.
'limits to' suggests removing the centre (the letters which limit the word).
'dud' with its centre taken out is 'dd'.
'rile' enclosing 'dd' is 'RIDDLE'.
(Other definitions for riddle that I've seen before include "Screen" , "Cryptic verse" , "Puzzling question - sieve" , "Sphinx's conundrum?" , "Cryptic question" .)