Minister raised in Old Testament? That's obvious (5)
I believe the answer is:
overt
'obvious' is the definition.
('overt' can be similar in meaning to 'obvious')
'minister raised in old testament?' is the wordplay.
'minister' becomes 'rev' (I've seen this before**).
'raised' says the letters should be written in reverse.
'in' is an insertion indicator.
'old testament?' becomes 'ot'.
'rev' back-to-front is 'ver'.
'ver' put into 'ot' is 'OVERT'.
'that's' is the link.
(Other definitions for overt that I've seen before include "Open, not 1 across" , "Conspicuous" , "Open, up front" , "Open and obvious" , "Plain to see - manifest" .)