How would a foreign princess married to a British peer be styled?

Let's say a British duke marries the daughter of a non-British reigning
sovereign, and that the married couple settle in the UK.

If the sovereign in question allowed his or her daughter to retain her royal
title and style following her marriage, would she automatically be allowed
to use it in the UK, or would she need the Queen's permission to do so?

I'm curious to know if she would be known as HRH The Princess X of Y, HRH
The Duchess of Z, HG The Duchess of Z or some other combination of these
styles.

(Gary Holtzman) garyholtzman...

This situation exists. The Marquess of Duoro, heir to the duke of Wellington, is
married to HRH Princess Antonia of Prussia. She is known as the Marchioness of

Guy Stair Sainty...

Not HRH,her parents marriage did not conform to the House Laws and she is just a
princess of Prussia without the HRH.

sionevar...

Is it correct that she was born and raised in the UK? If so, does this have
any impact on her status within the House? Are there residency/nationality
requirements?

Duoro and does not use her Prussian title in Britain.

the_verminator...

HRH Princess [Christian Name], Duchess of.........