Insist sports must involve cycling (5)
I believe the answer is:
swear
'insist' is the definition.
(thesaurus)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for swear that I've seen before include "Solemnly promise" , "Assert" , "Express annoyance" , "Use indecent or blasphemous language" , "Emit oath or take vow" .)