It's a luxury eating like a horse? Only the sides! (4)
I believe the answer is:
ease
'it's a luxury' is the definition.
(thesaurus)
'horse? only the sides' is the wordplay.
'horse?' becomes 'ea' (I am not sure about this - if you are sure you should believe this answer much more).
'only' becomes 'sole' ('sole' can be a synonym of 'only').
'the sides' says to hollow out the word (remove centre letters).
'sole' with its middle removed is 'se'.
'ea'+'se'='EASE'
'eating like a' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for ease that I've seen before include "Absence of effort" , "Affluence" , "Reduce (pain)" , "Comfort and repose" , "Leisure, relaxation" .)