Offer head sympathy (10)
I believe the answer is:
tenderness
'sympathy' is the definition.
(I know that tenderness is a type of compassion)
'offer head' is the wordplay.
'offer' becomes 'tender' (tender can mean to offer something).
'head' becomes 'ness' (ness is a headland).
'tender'+'ness'='TENDERNESS'
(Other definitions for tenderness that I've seen before include "Compassion" , "Gentle quality" , "sore?" , "Gentleness, sensitivity" , "Heart" .)