My question how can you describe it in a few words when you incline with your head that the person to leave without saying a word.
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Related notions are:
He waved me away and She nodded me away
(idiomatic) To reject or dismiss with a hand gesture
Nod = If you nod, you bend your head once, as a way of saying hello or goodbye
Hence nod away is to indicate goodbye and nod in is to invite in.
Google ngram has statistics for nod them away and shows examples such as
Any time someone approached, Ophelia groaned, and Colin nodded them away.
I might say motion (with the head).
Direct or command (someone) with a movement of the hand or head.
‘he motioned Dennis to a plush chair’