Day: the short period of time (5)
I believe the answer is:
month
'period of time' is the definition.
(month is a kind of period of time)
'day the short' is the wordplay.
'day' becomes 'mon' (**).
'short' means to remove the last letter.
'the' with its last letter removed is 'th'.
'mon'+'th'='MONTH'
(Other definitions for month that I've seen before include "Twelfth of a year" , "One of 12 divisions" , "Lunation" , "May, perhaps" , "See 10" .)