Outdoor broadcast introduced by old writer (4-3)
I believe the answer is:
open-air
'outdoor' is the definition.
(outdoor means out in the open air)
'broadcast introduced by old writer' is the wordplay.
'broadcast' becomes 'air' (to air on TV).
'introduced by' means one lot of letters go next to another.
'old' becomes 'o' (abbreviation).
'writer' becomes 'pen' (something which writes).
'o'+'pen'='open'
'air' after 'open' is 'OPEN-AIR'.
(Other definitions for open-air that I've seen before include "Exposed to the elements" , "Outdoor" , "outside" , "Taking place outdoors" , "Alfresco" .)