On the other hand, I recall from viewing numerous microfiche at the LDS Family History Centers, that the Hempsteads of New London and Long Island, New York went back and forth between the 2 locales quite regularly, including having their children baptised in both places. Thus it doesn't seem too far-fetched to think that the Hempsteads of Bklyn could have maintained a fairly close relationship with their New London relatives.
In looking for the parentage of Clement Miner, the only 2 possibilities appear to be Christopher Hempstead Sr., making Clement a brother of "my" Christopher Hempstead [Jr.], or Nathaniel Hempstead Jr. who married Mary Pedricks. Nathaniel Jr. died before 1820; Clement married Sarah Brown around 1834 and resided Long Island by 1840; at 1850 Nathaniel III was living with his mother in Bklyn. [He died 1870 and was buried in Riverhead, NY in Clement's family plot.]
Tracking Clement as a child in the earlier censuses [1810-1830] has not been totally successful. I cannot locate him at all in 1830, at least not as head of household, and not as a child at home with either Mary Hempstead or Christopher Hempstead Sr. In 1820, however, he fits into either household!
Clement's children, in order of birth, were: 2 children died as infants; Mary [named after his mother?], Clement Jr., Nathaniel [after his father?], Caroline, Sarah [after his wife], Anna [after his sister?], Lillian, and Eliza [after another sister?]. He only had 2 living sons, neither of whom was named Christopher.
Based on the names of Clement's children, and Nathaniel [III]'s burial in Clement's family plot in Riverhead, it appears to me that Clement was the son of Nathaniel Jr. and Mary, thus a brother of Nathaniel Hempstead III.
Clement Miner Hempstead and John Hempstead [son of Christopher Hempstead Jr.] were neighbors in Riverhead for years. Their relationship, based on the above supposition, would have been first cousins, once removed.