Rider, most outstanding, in demand perhaps (8)
I believe the answer is:
addendum
'rider' is the definition.
(thesaurus)
'most outstanding in demand perhaps' is the wordplay.
'most outstanding' becomes 'du' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'perhaps' indicates an anagram.
'demand' anagrammed gives 'addenm'.
'du' placed into 'addenm' is 'ADDENDUM'.
Can you help me to learn more?
(Other definitions for addendum that I've seen before include "Supplement, appendix" , "Postscript" , "Textual matter added on" , "Thing to be added" , "Something attached to the end, say of book" .)