Stays a desire for extra cycling clash (8)
I believe the answer is:
disagree
'clash' is the definition.
(thesaurus)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for disagree that I've seen before include "Differ, object" , "Differ in opinion" , "Beg to differ" , "Have conflicting opinions" , "source of conflict" .)