Brute for whom Beatrice hasn't a moment, by the way (5)
I believe the answer is:
beast
'brute' is the definition.
(I know that brute can be written as beast)
'beatrice hasn't a moment by the way' is the wordplay.
'hasn't' indicates named letters should be taken away.
'a moment' becomes 'trice' (I've seen this in another clue).
'by' says to put letters next to each other.
'the way' becomes 'st' (abbreviation for street).
'beatrice' with 'trice' removed is 'bea'.
'bea'+'st'='BEAST'
'for whom' is the link.
(Other definitions for beast that I've seen before include "Bully" , "Nasty type" , "Dangerous animal" , "Savage" , "horse?" .)