Note parent admits also supporting more cycling (10)
I believe the answer is:
memorandum
'note' is the definition.
(I know that memorandum is a type of note)
'parent admits also supporting more cycling' is the wordplay.
I cannot quite see how this works, but
'also' could be 'and' (I've seen this before) and 'and' is present in the answer.
an anagram of 'more' is 'emor' which is present in the answer.
'parent' could be 'mum' (mum is a kind of parent) and 'mum' is present in the remaining letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for memorandum that I've seen before include "Written message or note" , "brief note" .)