Little time to back up (6)
I believe the answer is:
second
'back up' is the definition.
(seconding is a kind of backing up)
'little time to' is the wordplay.
'little' means to remove the last letter (the word is not quite complete).
'time' becomes 'sec'.
'to' becomes 'cond' (I am not sure about this - if you are sure you should believe this answer much more).
'sec' with its last letter taken away is 'se'.
'se'+'cond'='SECOND'
Can you help me to learn more?
(Other definitions for second that I've seen before include "Lower < back" , "jiffy" , "Unsurpassed" , "Small fraction of a day" , "Assistant in the ring" .)