Annoying person's obnoxious roar at gag about neckline (10)

'annoying person's obnoxious roar' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'at gag about neckline' is the wordplay.
I cannot quite understand how this works, but
'at' is within the answer.
an anagram of 'gag' is 'agg' which is located in the answer.
'about' could be 'a' (abbreviation in Chambers) and 'a' is located in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?