Inside, theologians each study blind alleys (4,4)
I believe the answer is:
dead ends
'blind alleys' is the definition.
('dead end' can be a synonym of 'blind alley')
'inside theologians each study' is the wordplay.
'inside' is an insertion indicator.
'theologians' becomes 'DDs' (DD is short for Doctor of Divinity).
'each' becomes 'ea' (abbreviation).
'study' becomes 'den' (term for a study or office).
'ea'+'den'='eaden'
'dds' enclosing 'eaden' is 'DEAD-ENDS'.
(Other definitions for dead ends that I've seen before include "Unproductive results" , "Places or situations where further progress is impossible" , "Culs de sac?" , "situations offering no progress" , "Blind alleys or jobs with no prospects" .)