Sacred object in half of Islam, say? Christianity, primarily (5)
I believe the answer is:
relic
'sacred object' is the definition.
'half of islam say? christianity primarily' is the wordplay.
'half of' suggests halving the letters.
'islam say?' becomes 'religion' (islam is a kind of religion).
'primarily' indicates taking the first letters.
The first letter of 'christianity' is 'c'.
'religion' with half the letters taken is 'reli'.
'reli'+'c'='RELIC'
'in' is the link.
(Other definitions for relic that I've seen before include "Ancient survival" , "Venerated memento" , "Outdated survival" , "Item surviving from the past" , "Paper craft" .)