Barber upset oil initially on cloth provided (6)
I believe the answer is:
figaro
'barber' is the definition.
(main character in The Barber of Seville)
'upset oil initially on cloth provided' is the wordplay.
'upset' is a reversal indicator.
'initially' suggests taking the first letters.
'on' says to put letters next to each other.
'cloth' becomes 'rag' (rag is a kind of cloth).
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
The first letter of 'oil' is 'o'.
'o'+'rag'+'if'='oragif'
'oragif' in reverse letter order is 'FIGARO'.
(Other definitions for figaro that I've seen before include "Le -, French paper" , "Operatic character" , "hairdresser" , "The Barber of Seville" , "Mozart's 'Marriage'" .)