I’m opposed to that, not to cycling (4)
I believe the answer is:
nope
'i'm opposed to' is the definition.
I can't tell whether this defines the answer.
'not to cycling' is the wordplay.
'not' becomes 'no' (negative).
'to cycling' becomes 'pe' (I can't explain this - if you can you should believe this answer much more).
'no'+'pe'='NOPE'
'that' is the link.
Can you help me to learn more?
(Other definitions for nope that I've seen before include "Emphatically not!" , "not with stress" , "definitely not!" , "Negative response" , "Not on your life!" .)