Having nothing to do with it, a bicycle in pieces (8)
I believe the answer is:
celibacy
'having nothing to do with it' is the definition.
I can't judge whether this definition defines the answer.
'a bicycle in pieces' is the wordplay.
'in pieces' indicates anagramming the letters.
'a'+'bicycle'='abicycle'
'abicycle' with letters rearranged gives 'CELIBACY'.
Can you help me to learn more?
(Other definitions for celibacy that I've seen before include "nothing personal!" , "Chastity" , "Abstaining from sex" , "Unmarried state entered in to by some clergy" , "Unmarriied state for religious reasons" .)