Royal couple precede cook carrying one cover for crown (8)
I believe the answer is:
kerchief
'cover for crown' is the definition.
(item of clothing worn on the head or crown)
'royal couple precede cook carrying one' is the wordplay.
'royal couple' becomes 'ker' (I've seen this in other clues).
'precede' says to put letters next to each other.
'cook' becomes 'chef' (chef is a kind of cook**).
'carrying' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'chef' enclosing 'i' is 'chief'.
'ker'+'chief'='KERCHIEF'
(Other definitions for kerchief that I've seen before include "Covering" , "This covers head" , "Neck cloth" , "Square of cotton" , "Cloth cover for neck/head" .)