Dullness of doctor on backing theatre award (8)
I believe the answer is:
monotony
'dullness' is the definition.
(monotony can mean dullness or tedium)
'doctor on backing theatre award' is the wordplay.
'doctor' becomes 'mo' (medical officer).
'backing' says the letters should be written backwards.
'theatre award' becomes 'Tony' (as in the Tony Awards).
'on' backwards is 'no'.
'mo'+'no'+'tony'='MONOTONY'
'of' acts as a link.
(Other definitions for monotony that I've seen before include "Tedious lack of variety" , "Unvarying tedium" , "fixed routine" , "Tediousness" , "Lack of excitement" .)