Deep down that somehow engages listener (2,5)
I believe the answer is:
at heart
'deep down' is the definition.
('at heart' can be a synonym of 'deep down')
'that somehow engages listener' is the wordplay.
'somehow' indicates an anagram.
'engages' is an insertion indicator.
'listener' becomes 'ear' (I've seen this before).
'that' anagrammed gives 'atht'.
'atht' enclosing 'ear' is 'AT HEART'.
(Other definitions for at heart that I've seen before include "In one's real nature - a threat (anag)" , "In reality" , "In essence" , "A threat, in one's inmost feelings" , "In one's innermost feelings, in that era" .)