Organ, as it happens, close to altar (5)
I believe the answer is:
liver
'organ' is the definition.
(I know that liver is a type of internal organ)
'as it happens close to altar' is the wordplay.
'as it happens' becomes 'live' (as in live television).
'close to' says to take the final letters (the close of something is the end).
The last letter of 'altar' is 'r'.
'live'+'r'='LIVER'
(Other definitions for liver that I've seen before include "Large gland" , "Detoxifying organ" , "Organ; reddish-brown" , "Abdominal organ" , "Part of body" .)