Clue: Audibly expressed frustration with BBC4, perhaps (4)
Answer: SIDE
Explanation: Definition: BBC4, perhaps
Sounds like ('audibly') SIGHED ('expressed frustration'); among the various meanings of SIDE in Chambers is "a television channel (*inf)*". I suppose that dates from when there were just two channels – "I don't think much of this programme, let's see what's on the other side".