For each person having no heir (3)
I believe the answer is:
per
'for each' is the definition.
('per' can mean for each)
'person having no heir' is the wordplay.
'having no' indicates named letters should be taken away.
'heir' becomes 'son' (I've seen this before).
'person' with 'son' removed is 'PER'.
(Other definitions for per that I've seen before include "According to" , "For each or every" , "Preposition meaning for each" , "Preposition indicating by means of" .)