### Clue: A legendary DJ's spinning some R.E.M.? (5)
### Answer: SLEEP 
 ### Explanation: Definition: some R.E.M
 **Reversal of**(… spinning) [ PEEL(John, legendary disc jockey with BBC Radio 1)'S ].
Defn: …, not the alternative-rock band, but the sleep phase characterised by Rapid Eye Movement, and dreaming.