Involve deeply in some dimmer sense (7)
I believe the answer is:
immerse
'involve deeply' is the definition.
(I've seen this before)
'in some dimmer sense' is the wordplay.
'in' indicates the answer is hidden within the clue.
'IMMERSE' can be found hidden inside 'some dimmer sense'.
(Other definitions for immerse that I've seen before include "Submerge in water or liquid" , "Cover with water, dip into" , "Submerge in water as once for baptism" , "Engross" , "Drown" .)