Existential statement has at first mystified prayer leader (4)
I believe the answer is:
imam
'prayer leader' is the definition.
(I've seen this in another clue)
'existential statement has at first mystified' is the wordplay.
'existential statement' becomes 'iam' (I've seen this in another clue).
'has' indicates putting letters inside.
'at first' says to take the initial letters.
The initial letter of 'mystified' is 'm'.
'iam' enclosing 'm' is 'IMAM'.
(Other definitions for imam that I've seen before include "Muslim prayer leader" , "Caliph" , "Islamic prayer leader" , "Man who leads prayers in a mosque" , "Muslim cleric" .)