Hide classical object of worship going west, then east (5)
I believe the answer is:
suede
'hide' is the definition.
(suede is a material made from an animal's hide)
'classical object of worship going west then east' is the wordplay.
'classical object of worship' becomes 'deus' ('god' in Latin, a classical language).
'going west' says the letters should be written in reverse.
'then' says to put letters next to each other.
'east' becomes 'e' ('E' can be a synonym of 'east').
'deus' backwards is 'sued'.
'sued'+'e'='SUEDE'
(Other definitions for suede that I've seen before include "unprepared material" , "Form of leather" , "Leather with velvety nap used in shoes and clothes" , "Soft goatskin" , "Leather with a soft napped surface" .)