Organ installed in empty hut’s centre (5)
I believe the answer is:
heart
'centre' is the definition.
(synonyms)
'organ installed in empty hut's' is the wordplay.
'organ' becomes 'ear' (ear is a kind of organ).
'installed in' is an insertion indicator.
'empty' means to remove the middle letters.
'hut' with its middle taken out is 'ht'.
'ear' going inside 'ht' is 'HEART'.
(Other definitions for heart that I've seen before include "Cardiac courage" , "Red card" , "one in suit" , "Not a club" , "Spirit - core" .)