Angry about no good, thankless person (7)
I believe the answer is:
ingrate
'thankless person' is the definition.
(I've seen this before)
'angry about no good' is the wordplay.
'angry' becomes 'irate' (similar in meaning).
'about' means one lot of letters goes inside another.
'no' becomes 'n' (common abbreviation).
'good' becomes 'g' (abbreviation).
'n'+'g'='ng'
'irate' placed around 'ng' is 'INGRATE'.
(Other definitions for ingrate that I've seen before include "One who never says thanks" , "One unappreciative" , "Thankless wretch" , "No thanks, I say!" , "Does one not appreciate" .)