Half a mile in a month? – and the rest! (5)
I believe the answer is:
sleep
'the rest' is the definition.
('sleep' can be a synonym of 'rest')
'half a mile in a month?' is the wordplay.
'half a' indicates taking half.
'in' indicates putting letters inside.
'a month?' becomes 'sep' (Sep is an example**).
'mile' with half the letters taken is 'le'.
'le' put inside 'sep' is 'SLEEP'.
'and' is the link.
(Other definitions for sleep that I've seen before include "Doze, nap" , "Natural state of unconscious rest" , "Drop off" , "Wayne _; former Royal Ballet principal dancer" , "Be dormant" .)