Approaches one's heart of hearts in various ways (5)
I believe the answer is:
nears
'approaches one's' is the definition.
'nears' can be an answer for 'approaches' ('near' can be a synonym of 'approach'). I am not sure about the 'one's' bit.
'heart of hearts in various ways' is the wordplay.
'heart of' says to take the centre.
'in' indicates putting letters inside.
'various ways' becomes 'nes' (compass directions).
The middle of 'hearts' is 'ar'.
'ar' going into 'nes' is 'NEARS'.
Can you help me to learn more?
(Other definitions for nears that I've seen before include "Saner (anag.)" , "Comes closer" , "Bears down" , "Uses snare to get closer" , "Gets closer" .)