Vegetable matter a domestic animal has eaten (4)
I believe the answer is:
peat
'vegetable matter' is the definition.
'peat' can be an answer for 'matter' (peat is a kind of matter). I'm not sure about the 'vegetable' bit.
'a domestic animal has eaten' is the wordplay.
'a domestic animal' becomes 'pet' (I've seen this before).
'has' means one lot of letters goes inside another.
'eaten' becomes 'a' (I can't justify this - if you can you should give a lot more credence to this answer).
'pet' going around 'a' is 'PEAT'.
Can you help me to learn more?
(Other definitions for peat that I've seen before include "Dried plant material used as fuel" , "Tape around turf" , "Vegetable matter in bogs, like turf" , "Some got energy from this" , "Partially carbonised vegetable matter saturated with water" .)