Old instrument produced by theatres not in Harley Street (4)
I believe the answer is:
lyre
'old instrument' is the definition.
(I've seen this before)
'theatres not in harley street' is the wordplay.
'not in' is a deletion indicator.
'harley'+'street'='harleystreet'
'harleystreet' with 'theatres' taken away is 'LYRE'.
'produced by' acts as a link.
(Other definitions for lyre that I've seen before include "Old stringed instrument" , "Ancient stringed musical instrument with U-shaped frame" , "Harp used by ancient Greeks" , "Ancient musical instrument - sounds mendacious" , "used to produce music" .)