One short day is less than a month (3)
I believe the answer is:
mon
'one short day' is the definition.
(abbreviation for Monday; 'short' asks for a short form)
'less than a month' is the wordplay.
'less' is a deletion indicator.
'a' becomes 'an'.
'an'+'month'='anmonth'
'anmonth' with 'than' taken away is 'MON'.
'is' is the link.
(Other definitions for mon that I've seen before include "Ynys -- (Anglesey)" , "My resting-place (French)" , "Abbrev. for weekday or colloquial Scots male" .)