I'm having a morning with a holy man (4)
I believe the answer is:
imam
'a holy man' is the definition.
(Muslim preacher)
'i'm having a morning' is the wordplay.
'having' says to put letters next to each other.
'a morning' becomes 'am' (as in 12:00 AM).
'im'+'am'='IMAM'
'with' acts as a link.
(Other definitions for imam that I've seen before include "Prayer-leader in a mosque" , "Islamic minister" , "Maim (anag)" , "Prayer leader in a mosque" , "Muslim community leader" .)