Nothing but the deepest affection (4)
I believe the answer is:
love
This might be a double definition.
'nothing' is the first definition.
(love is zero in tennis)
'the deepest affection' is the second definition.
'love' can be an answer for 'affection' (I've seen this before). I am unsure of the 'the deepest' bit.
'but' acts as a link.
Can you help me to learn more?
(Other definitions for love that I've seen before include ""Tell me the truth about ___" (Auden)" , "No points" , "See 10" , "Zero score (it's all you need)" , "Score of zero at tennis" .)