Agree to cut frame Bogart bungled, embracing a star (5,5)
I believe the answer is:
greta garbo
'star' is the definition.
(I know that Greta Garbo was a movie star)
'agree to cut frame bogart bungled embracing a' is the wordplay.
'to cut frame' means to look at the middle letters (letters which frame the word are removed).
'bungled' is an anagram indicator.
'embracing' indicates putting letters inside.
The middle of 'agree' is 'gre'.
'gre'+'bogart'='grebogart'
'grebogart' anagrammed gives 'gretgarbo'.
'gretgarbo' going around 'a' is 'GRETA GARBO'.
(Other definitions for greta garbo that I've seen before include "See actress" , "Old actress" .)