For each person with no heir (3)
I believe the answer is:
per
'for each' is the definition.
(thesaurus)
'person with no heir' is the wordplay.
'with no' is a deletion indicator.
'heir' becomes 'son' (I've seen this before).
'person' with 'son' taken away is 'PER'.
(Other definitions for per that I've seen before include "Preposition indicating by means of" , "According to" , "Preposition meaning for each" , "For each or every" .)