Grub finally reaching organ, stomach (4)
I believe the answer is:
bear
'stomach' is the definition.
('bear' can be a synonym of 'stomach')
'grub finally reaching organ' is the wordplay.
'finally' suggests the final letters.
'reaching' means one lot of letters go next to another.
'organ' becomes 'ear' (ear is a kind of organ**).
The last letter of 'grub' is 'b'.
'b'+'ear'='BEAR'
(Other definitions for bear that I've seen before include "Beast - tolerate" , "Carry, convey" , "It may be polar or grizzly" , "Support (a weight)" , "Ursine animal" .)