Angry thief quietly put away (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'thief quietly put away' is the wordplay.
'thief' becomes 'pirate' (pirates are thieves).
'quietly' becomes 'p' (p for piano and quiet).
'put away' is a deletion indicator.
'pirate' with 'p' removed is 'IRATE'.
(Other definitions for irate that I've seen before include "Extremely angry" , "having got in wax" , "Wild" , "I tear away, being annoyed" , "Wrathful" .)