Queen's daughter left after first half of Chas & Dave ? (7)
I believe the answer is:
channel
'dave ?' is the definition.
(UK TV channel)
'queen's daughter left after first half of chas' is the wordplay.
'queen's daughter' becomes 'anne' (Princess Anne).
'left' becomes 'l' (common abbreviation).
'after' means one lot of letters go next to another.
'first half of' suggests halving the letters.
'chas' cut in half is 'ch'.
'anne'+'l'='annel'
'annel' put after 'ch' is 'CHANNEL'.
(Other definitions for channel that I've seen before include "Strait, (data) path" , "Length of water between two land masses" , "Bed of a stream; medium" , "TV station; direct towards an end" , "Medium of transmission" .)