Okay, no progress at all with William's other children with Elizabeth, but . . .

possible first marriage:

Lydney: September 21, 1805 William Clarke and Hanna Williams

Children: Thomas Clarke, b. June 19,1806, bap. Blakeney Chapel, Parents Wm & Hanna
Ann Clarke, b. Jan 8, 1809, bap. Blakeney Chapel, parents Wm & Hanna

(note: Thomas' father is listed as Thomas, but his mother is listed
as Hanna formerly Williams, so I think it should have been William.)

Death: Ann Clarke, April 16, 1812 age 3, daughter of William Clarke of Awre
Hanna Clarke, 20 March 1812, wife of William (Forest) Awre

The other less likely possibility was a marriage recorded in Newent between a William Clarke and Mary Tomkins on May 17, 1802. She was buried July 3, 1809, Westbury-on-Severn, also listed as wife of William Clarke.