Part of the body, part that aches terribly (5)
I believe the answer is:
chest
'part of the body' is the definition.
(chest is a part of the body)
'part that aches terribly' is the wordplay.
'part' indicates a hidden word.
'CHEST' is hidden within 'that aches terribly'.
(Other definitions for chest that I've seen before include "Large, sturdy box with a lid" , "Trunk or crate" , "It's enclosed by the ribs" , "Breast - case" , "Treasure (or heart) container" .)