Lively horse loses right plate (4)
I believe the answer is:
shoe
'plate' is the definition.
(shoe is a kind of plate)
'lively horse loses right' is the wordplay.
'lively' indicates an anagram (I've seen this in other clues).
'loses' suggests deleting specific letters.
'right' becomes 'r' (common abbreviation).
'horse' with 'r' removed is 'hose'.
'hose' with letters rearranged gives 'SHOE'.
(Other definitions for shoe that I've seen before include "mule, perhaps?" , "Pump, for example" , "Oxford, for instance" , "Camera mounting" , "One of a pair to wear" .)