Theologist invested in home improvements very little (5)
I believe the answer is:
diddy
'very little' is the definition.
'theologist invested in home improvements' is the wordplay.
'theologist' becomes 'dd' (Doctor of Divinity).
'invested in' is an insertion indicator.
'home improvements' becomes 'diy' (DIY is do-it-yourself work done on the home).
'dd' inserted into 'diy' is 'DIDDY'.
(Other definitions for diddy that I've seen before include "fool" , "Little" .)