Submit letters, capturing his heart (5)
I believe the answer is:
posit
'submit' is the definition.
(I know that submit can be written as posit)
'letters capturing his heart' is the wordplay.
'letters' becomes 'post' (letters in the mail or post).
'capturing' means one lot of letters goes inside another.
'heart' says to take the centre.
The middle of 'his' is 'i'.
'post' enclosing 'i' is 'POSIT'.
(Other definitions for posit that I've seen before include "Suggest" , "Lay down or assume (as the basis for an argument)" , "forward-looking statement" , "Propose" , "Put forward as true" .)