Fig.: asking someone, in a humble or submissive manner, to give you something or to do something for you.

A few months ago, I left my job with the arrogant claim that I would never return. But today, having found nothing else, I have to go back to my old boss hat in hand and ask for my job back

Qualche mese fa, mi sono licenziato dicendo arrogantemente che non sarei mai più ritornato. Ma oggi, non avendo trovato niente altro, mi ritrovo a dover andare dal mio vecchio capo con il cappello in mano e chiedere che mi riprenda al lavoro

The delegation will not go hat in hand to the negotiating table trying to redeem the trade war, but will assert its terms

La delegazione non andrà col cappello in mano al tavolo dei negoziati per cercare di redimere la guerra commerciale, ma farà valere le sue condizioni

The removal of one's hat is a gesture of respect, and our expression, used figuratively, is based on the image of someone standing, humbly, in front of a powerful person, asking for something