To brag about being a great star (6)

I believe the answer is:

bogart

I'm a little stuck... Click here to teach me more about this clue!

'a great star' is the definition.
'bogart' can be an answer for 'star' (Humphrey Bogart 1889-1957). I'm not certain of the 'a great' bit.

'to brag about' is the wordplay.
'about' indicates an anagram.
'to'+'brag'='tobrag'
'tobrag' is an anagram of 'BOGART'.

'being' acts as a link.

Can you help me to learn more?

(Other definitions for bogart that I've seen before include "Humphrey --, US film actor" , "Lauren Bacall's first actor husband, d. 1957" , "Rob gat from the old film star" , "Famous player" , "American actor" .)

I've seen this clue in the Evening Standard.

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