Blackbeard, say, doesn't start being angry (5)
I believe the answer is:
irate
'angry' is the definition.
(similar in meaning)
'blackbeard say doesn't start' is the wordplay.
'blackbeard say' becomes 'pirate' (Blackbeard was an 18th-century pirate).
'doesn't start' means to remove the first letter.
'pirate' with its initial letter taken off is 'IRATE'.
'being' is the link.
(Other definitions for irate that I've seen before include "Aggrieved" , "I tear away, being annoyed" , "Full of 22" , "Annoyed, exasperated" , "having got in wax" .)