Present participle of 'heir' used as a verb; the act of inheriting or being in the process of becoming an heir.
From 'heir' as a verb (itself from Old French 'eir,' Latin 'heres') plus the present participle suffix '-ing,' though this form is extremely archaic and rarely appears in modern English.
This might be the only time you'll encounter 'heiring' outside of a historical text or a very creative writer trying to sound medieval—it's a word that sounds made-up because English stopped using it centuries ago.
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