Dirge, primarily, in Ring Cycle (5)
I believe the answer is:
pedal
'cycle' is the definition.
(I've seen this before)
'dirge primarily in ring' is the wordplay.
'primarily' suggests taking the first letters.
'in' indicates putting letters inside.
'ring' becomes 'peal' ('peal' can be a synonym of 'ring'**).
The first letter of 'dirge' is 'd'.
'd' going within 'peal' is 'PEDAL'.
(Other definitions for pedal that I've seen before include "cause a revolution in cycling?" , "Foot control" , "Foot-operated lever" , "One may be sustaining" , "Plead for bike pusher" .)