A lover of priestess carrying cross for great king (9)
I believe the answer is:
alexander
'great king' is the definition.
(Alexander the Great)
'a lover of priestess carrying cross' is the wordplay.
'lover of priestess' becomes 'leander' (lover of the priestess Hero in Greek myth).
'carrying' indicates putting letters inside.
'cross' becomes 'x' (X is cross-shaped).
'leander' going around 'x' is 'lexander'.
'a'+'lexander'='ALEXANDER'
'for' is the link.
(Other definitions for alexander that I've seen before include "Healing process based on improving posture" , "Field marshal" , "Conquering Macedonian" , "The Great conqueror of Greece and Egypt and Persia" , "King of Macedon, conqueror of Greece, Egypt and Persia, d. 323 BC" .)