Farm animal faces horrid existence in field eating roots (6)
I believe the answer is:
heifer
'farm animal' is the definition.
(I've seen this before)
'faces horrid existence in field eating roots' is the wordplay.
'faces' says to take the initial letters (I've seen 'face of' mean this).
The initial letters of 'horrid existence in field eating roots' is 'HEIFER'.
(Other definitions for heifer that I've seen before include "part of stock" , "Young cow which has not yet given birth" , "a little lower" , "Female bovine that has not given birth" , "Farm animal" .)