She's a month at a loose end (4)
I believe the answer is:
jane
'she's' is the definition.
'a month at a loose end' is the wordplay.
'a month' becomes 'jan' (Jan is short for January).
'at' says to put letters next to each other.
'end' indicates one should take the final letters.
The last letter of 'loose' is 'e'.
'jan'+'e'='JANE'
(Other definitions for jane that I've seen before include "See 1" , "- - Eyre" , "Henry's third" , "- Austen, novelist" , "Plain --; -- Seymour" .)