Be quick to finish up in a state of rust (5)
I believe the answer is:
spurt
'a state of rust' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'be quick to finish up in' is the wordplay.
'be quick' becomes 'fast' (similar in meaning).
'to finish' suggests halving the letters.
'up' becomes 'pur' (I am not sure about this - if you are sure you should believe this answer much more).
'in' means one lot of letters goes inside another.
'fast' cut in half is 'st'.
'st' enclosing 'pur' is 'SPURT'.
Can you help me to learn more?
(Other definitions for spurt that I've seen before include "Short spell of increased speed" , "Gush out suddenly" , "Jet, gush" , "Gush; sudden burst" , "A short burst of activity" .)