Almost a frame of mind to make a beastly noise (3)
I believe the answer is:
moo
'a beastly noise' is the definition.
(noise made by a cow)
'almost a frame of mind' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'a frame of mind' becomes 'mood' (I've seen this before).
'mood' with its last letter removed is 'MOO'.
'to make' acts as a link.
(Other definitions for moo that I've seen before include "Cow's low" , "Irritating woman" , "Farmyard sound" , "Cow's call" , "Guernsey noise?" .)