Quick bite bishops demanded in middle of river (6)
I believe the answer is:
nibble
'quick bite' is the definition.
'nibble' can be an answer for 'bite' (nibbling is a kind of biting). I am unsure of the 'quick' bit.
'bishops demanded in middle of river' is the wordplay.
'bishops' becomes 'bb' (a chess abbreviation for bishop written twice).
'demanded' becomes 'nil' (I can't justify this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'middle of' says to take the centre.
'river' becomes 'dee' (River Dee).
The centre of 'dee' is 'e'.
'bb' going inside 'nil' is 'nibbl'.
'nibbl'+'e'='NIBBLE'
Can you help me to learn more?
(Other definitions for nibble that I've seen before include "Take small bites of" , "express tentative interest" , "Snack" , "Bite gently and eat a little at a time" , "Take tiny bites" .)