Extra study adopted by a theologian, with some hesitance (8)
I believe the answer is:
addendum
'extra' is the definition.
(I've seen this before)
'study adopted by a theologian with some hesitance' is the wordplay.
'study' becomes 'den' (I've seen this before**).
'adopted by' means one lot of letters goes inside another (I've seen this in other clues).
'theologian' becomes 'dd' (Doctor of Divinity degree).
'with' says to put letters next to each other.
'some hesitance' becomes 'um' (expression of hesitation).
'a'+'dd'='add'
'den' put into 'add' is 'addend'.
'addend'+'um'='ADDENDUM'
(Other definitions for addendum that I've seen before include "Additional material at the end" , "something tacked on" , "Supplementary text tacked on to the end" , "Supplement to a book" , "Something attached to the end, say of book" .)