Quickly set off for the outskirts (6)
I believe the answer is:
presto
'quickly' is the definition.
(I've seen this in another clue)
'set off for the outskirts' is the wordplay.
I cannot quite see how this works, but
an anagram of 'set' is 'est' which is located in the answer.
'for' could be 'pro' (as in being 'pro' or in favour of something) and 'pro' is present in the leftover letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for presto that I've seen before include "Very fast (mus.)" , "(In music) fast" , "quickly in bars" , "Hey, it's a magician's word" , "Immediately" .)