A pair I left for a month (5)
I believe the answer is:
april
'for a month' is the definition.
(April is an example)
'a pair i left' is the wordplay.
'pair' becomes 'pr' (abbreviation).
'left' becomes 'l' (common abbreviation).
'a'+'pr'+'i'+'l'='APRIL'
(Other definitions for april that I've seen before include "days on end" , "'All in an ... evening' (Katharine Tynan)" , "Girl" , "Start of the financial year" , "Part of spring" .)