Speed with which a rodent takes the last of the cheese (4)
I believe the answer is:
rate
'speed' is the definition.
(the speed at which something happens)
'a rodent takes the last of the cheese' is the wordplay.
'a rodent' becomes 'rat' (rat is a kind of rodent).
'takes' means one lot of letters go next to another.
'the last of' suggests the final letters.
The last letter of 'cheese' is 'e'.
'rat'+'e'='RATE'
'with which' acts as a link.
(Other definitions for rate that I've seen before include "Velocity" , "Bawl out" , "Tariff" , "Assign a value to something" , "Judge" .)