Important, almost bald Arab backing play (5,7)
I believe the answer is:
major barbara
'play' is the definition.
(I've seen this before)
'important almost bald arab backing' is the wordplay.
'important' becomes 'major' (major can mean of great importance).
'almost' means to remove the last letter (most of the word but not all of it).
'bald' becomes 'bare' (synonyms).
'backing' is a reversal indicator.
'arab' backwards is 'bara'.
'bare' with its final letter taken away is 'bar'.
'major'+'bar'+'bara'='MAJOR BARBARA'
(Other definitions for major barbara that I've seen before include "G.B. Shaw play" , "GBS Salvation Army heroine" .)