Each sound is a sound of contentment (4)
I believe the answer is:
Here is my best explanation:
'a sound of contentment' is the definition.
'each sound' is the subsidiary indication.
'each' becomes 'per'.
'sound' indicates a 'sounds like' (homophone) clue.
'per' is a homophone of 'purr'.
'is' is the link.
(Other definitions for purr that I've seen before include "Sound of happy animal", "Happy feline sound", "Low vibratory sound", "Feline sound", "Tiddles' sound", "Soft noise of engine", "Appreciative feline sound", "Noise of a cat", "Engine sound" and "content? I might".)