Absent-minded head of BBC came down after broadcast (14)
I believe the answer is:
scatterbrained
'absent-minded' is the definition.
(I've seen this before)
'head of bbc came down after broadcast' is the wordplay.
'head of' says to take the initial letters.
'came down' becomes 'rained' (raining is a kind of coming down).
'after' says to put letters next to each other.
'broadcast' becomes 'scatter' (broadcast can mean to scatter seeds).
The initial letter of 'bbc' is 'b'.
'b'+'rained'='brained'
'brained' put after 'scatter' is 'SCATTERBRAINED'.
(Other definitions for scatterbrained that I've seen before include "Careless" , "Inclined to forget" , "easily distracted - with 20d" , "poorly focused on the task?" , "Disorganised and unable to concentrate" .)