The Clifford Baronetcy, of the Navy was created for Augustus William James Clifford, the illegitimate son of the 5th Duke of Devonshire (as son of the 6th Baroness Clifford and himself the 7th one) on August 4 1838 in the Baronetage of the United Kingdom. It has become extinct at the death of the 4th Baronet on 22 November 1895.
The Clifford Baronetcy, of Flaxbourne in New Zealand was created for Charles Clifford, a grand-nephew of the 4th Baron Clifford of Chudleigh (and nephew of Sir Thomas Clifford-Constable, Bt) on July 16 1887 in the Baronetage of the United Kingdom. As of 2007, the baronetcy is held by the 7th Baronet.
The current heir presumptive to the title is his twin brother Charles Joseph Clifford.¹
¹According to this and that information the current baronet has not any issue, so his brother is the next in line. If you have more recent and better information, please feel free to improve this article.