A bicycle for travel? Not having it (8)
I believe the answer is:
celibacy
'not having it' is the definition.
('it' can mean sex)
'a bicycle for travel?' is the wordplay.
'for travel?' indicates anagramming the letters (letters travelling around).
'a'+'bicycle'='abicycle'
'abicycle' with letters rearranged gives 'CELIBACY'.
(Other definitions for celibacy that I've seen before include "Unmarried state on a bicycle" , "Abstention from the other" , "nothing personal!" , "requirement for RC priest" , "Abstaining from sex" .)