Classic music genre rejected by Roosevelt, briefly (3,4)
I believe the answer is:
the oaks
'classic' is the definition.
(I've seen this before)
'music genre rejected by roosevelt briefly' is the wordplay.
'music genre' becomes 'ska' (I've seen this before).
'rejected' shows that the letters should be reversed in order.
'by' is a charade indicator (letters next to each other).
'roosevelt briefly' becomes 'theo' (Theodore Roosevelt 26th US President).
'ska' back-to-front is 'aks'.
'aks' after 'theo' is 'THE OAKS'.
(Other definitions for the oaks that I've seen before include "Race run at Epsom" , "growing from the humblest beginnings" , "Classic English horse race" , "One particular stand" , "Race held at Epsom" .)