Born on the first of December, in poverty (4)
I believe the answer is:
need
'poverty' is the definition.
(need is a kind of poverty)
'born on the first of december' is the wordplay.
'born' becomes 'nee' ('nee' is 'born' in French).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'the first of december' becomes 'd' (1st letter of 'december').
'nee'+'d'='NEED'
'in' acts as a link.
(Other definitions for need that I've seen before include "privation" , "Lack or require" , "Exigency" , "Necessity" , "''A friend in .... is a friend indeed''" .)