Moved quickly - discovered with time to spare (5)
I believe the answer is:
raced
'moved' is the definition.
(racing is a kind of moving)
'quickly discovered with time to spare' is the wordplay.
'quickly' becomes 'express' (I've seen this before).
'discovered' says to take the centre (dis-covered - outer letters removed).
'with time to spare' becomes 'aced' (I am not sure about this - if you are sure you should believe this answer much more).
The middle of 'express' is 'r'.
'r'+'aced'='RACED'
Can you help me to learn more?
(Other definitions for raced that I've seen before include "Took part in speed contest" , "Dashed" , "Competed" , "Travelled at speed" , "Operated at excessive speed" .)