Born at the back of beyond, in poverty (4)
I believe the answer is:
need
'poverty' is the definition.
(I know that need is a type of poverty)
'born at the back of beyond' is the wordplay.
'born' becomes 'nee' ('nee' is 'born' in French).
'at the back of' says to take the final letters (I've seen 'at the back' mean this).
The final letter of 'beyond' is 'd'.
'nee'+'d'='NEED'
'in' is the link.
(Other definitions for need that I've seen before include "What's lacking" , "Necessity" , "Rely on" , "Want - require(ment)" , "Distressful situation" .)