An NRI can be, and stay, karta
Start with the myth: that an NRI cannot be karta. Nothing in the Income-tax Act, the Hindu Succession Act or the exchange-control law says so. Under general Hindu law the karta is ordinarily the senior-most coparcener of the family, and a non-resident senior-most coparcener holds that position like anyone else. Your being abroad does not strip your coparcenary rights, which arise by birth, and since the 2005 amendment daughters, including NRI daughters, are coparceners too and can be karta.
What non-residence affects is the practicality, not the eligibility. A karta who cannot manage the family's affairs day to day from abroad can, under general Hindu law, have a junior coparcener act as karta with the consent of the others. So the family can keep functioning smoothly with someone in India handling matters, without you having to give up the position. The eligibility is settled; the arrangement is what you plan around.
Your residence is not the HUF's residence
The bigger misunderstanding is that an NRI karta makes an NRI HUF. It does not, and this matters for tax. An HUF is a separate taxpayer, and its residence is decided by where its control and management sit, not by where the karta lives. As long as any part of the HUF's control and management is in India, a coparcener taking decisions there, the banking and the assets handled in India, the HUF stays resident, whatever the karta's own status.
So a family with an NRI karta abroad but its affairs run from India remains a resident HUF, taxed the ordinary way. Only if the control and management shift wholly outside India does the HUF become non-resident. This separation is genuinely useful: it means moving abroad does not, by itself, change your family HUF's tax position, and it is worth understanding before assuming otherwise. The detail of that test is its own subject, covered in the residential-status page.