Procession heading off for monument (4)
I believe the answer is:
arch
'monument' is the definition.
(thesaurus)
'procession heading off' is the wordplay.
'procession' becomes 'march' (march is a kind of procession).
'heading off' means to remove the first letter.
'march' with its initial letter taken off is 'ARCH'.
'for' is the link.
(Other definitions for arch that I've seen before include "Curved spanning structure" , "Instep of foot" , "one under a foot?" , "architectural feature" , "Self-consciously playful or teasing" .)