Overthrown monarchy welcomes son; he had lost his birthright (4)
I believe the answer is:
esau
'he had lost his birthright' is the definition.
(Esau lost his birthright in the Bible)
'overthrown monarchy welcomes son' is the wordplay.
'overthrown' shows that the letters should be reversed in order.
'monarchy' becomes 'UAE' (the United Arab Emirates is a monarchy).
'welcomes' is an insertion indicator (in sense of 'invites in').
'son' becomes 's' (genealogical abbreviation for son).
'uae' going around 's' is 'uase'.
'uase' back-to-front is 'ESAU'.
(Other definitions for esau that I've seen before include "Hairy brother to Jacob in Bible" , "Hairy OT character" , "Jacob's brother (OT)" , "Jacob's brother in the bible" , "Cunning hunter" .)