Miss being born on the first of December (4)
I believe the answer is:
need
'miss' is the definition.
(I've seen this before)
'born on the first of december' is the wordplay.
'born' becomes 'nee' ('nee' is 'born' in French).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'the first of december' becomes 'd' (1st letter of 'december').
'nee'+'d'='NEED'
'being' acts as a link.
(Other definitions for need that I've seen before include "What's lacking" , "Require (as essential)" , "Call" , "A condition" , "Necessitate" .)