A divine increase (3)
I believe the answer is:
add
'increase' is the definition.
(I've seen this before)
'a divine' is the wordplay.
'divine' becomes 'dd' (divine can mean theologian eg Doctor of Divinity).
'a'+'dd'='ADD'
(Other definitions for add that I've seen before include "Sum up; say further" , "Contribute" , "Combine (numbers)" , "Count up" , "Determine the sum of" .)