Ring cycle has no heart (4)
I believe the answer is:
peal
'ring' is the definition.
(synonyms)
'cycle has no heart' is the wordplay.
'cycle' becomes 'pedal' (synonyms).
'has no heart' suggests removing the centre.
'pedal' with its middle taken out is 'PEAL'.
(Other definitions for peal that I've seen before include "Set of bells for ringing" , "Thunderous roar" , "Ring (of bell), clap (of thunder)" , "(Bells) ring" , "Sound of bells, thunder" .)