What if HRH Prince Henry married a Princess of Leitchstein ...She 23 and he 32,What reign would he become part of Britain or Leitchstein?

Harry remains a prince of the United Kingdom and a successor to the British throne; the Princess from Liechtenstein would remain a successor to her principality's throne, but she would become Harry's consort and would be expected to accept the UK as her country.

The countries would remain separate.

Harry would remain a prince of the UK and since he won't be king, he won't be reigning anywhere.

Women assume the rank and titles of their husbands, even HM The Queen became the Duchess of Edinburgh upon her marriage and it was not until after she became Queen that she outranked her husband.

Harry would impregnate a new royal line.

The british royal family is already set.