The patriarchal pedigrees seem to show this Alexander as a son of one James McClure (d 1799) Augusta Co and a wife Alice Young. This seems to represent multiple mistakes. Alice Young was married to one Halbert McClure, killed by the Indians in SW Virginia in 1782. There was a James McClure who died in Augusta Co Va 13 Sep 1799. His estate was the subject of various records including a lawsuit in the 1820's (Cf Chalkley, CHRONICLES OF THE SCOTCH IRISH SETTLEMENT IN VIRGINIA, Vol 1, page 427) which reveal that James McClure left a widow Elizabeth and children: Andrew, John, Margaret, James, Samuel, Josiah, Eleanor, and Elizabeth (the latter two infants). This James was probably part of the old McClure family of upper Augusta whose land remained in Augusta after many other counties were taken off of Augusta. The Halbert McClure clan lived on the Borden tract which first became Botetourt Co and later Rockbridge Co.
Others show the above Alexander McClure as a son of Moses McClure, died 1778, but a researcher named Bob Weiss has posted a useful article entitled THE ALEXANDER MCCLURE QUANDARY in which he seems to make a case for a different Alexander being Moses's son.
The most likely parentage for the above Alexander McClure of Grant Co seems to me to be Alexander McClure (son of Halbert) whose will was proved in Rockbridge Co in 1790 (written in 1787). It shows that his son, Alexander, was still a minor in 1787. Also, he and his other underage brothers were left "land in Kentucky".
I have not made an exhaustive study of this identification, but it seems the most likely placement for Alexander of Grant Co.
Alexander McClure Sr (son of Halbert) was first married to a wife name Susannah and then by 1773 married a much younger second wife, Martha Moore, by whom he had five children or so.