Hannah's parentage has long been a puzzle.  I have checked all entries of the following surnames in Essex, Suffolk , Middlesex, Norfolk & Plymouth counties in Eastern, MA:  Preast, Preest, Preist, Prest, Preush, Priest, Priesst.

After writing down everything of even remote relevance and then distilling it, here are the possibilities.

John Priest married his first wife Elizabeth Gray on 25 February 1672/3 in Salem, Essex co., MA.  The children recorded in Salem VRs are Elizabeth (born on 29 January 1679/80) and Hanna (baptized in October 1689).  It appears that John's wife Elizabeth belonged to the Salem Church, since their daughter Elizabeth was baptized as "d. El." in August of 1680.

Elizabeth, Sr. died before 1699/1700, when John remarried to the widow Hannah (MeachaM) Gill, [widow of William Gill] on 4 March 1699/1700 in Salem.

If the first Hannah had died and they had a second child named Hannah, this could concievably be the Hannah Preast who married John Hawkes.

A more realistic parentage is this:

Joseph Priest married Hannah Hager (1649-1702, Watertown) by 1678/9 in Boston.  They had a son named Joseph on 18 March 1678 and a daughter named Hannah on 20 March 1681.  Both born in Boston.

I believe it was this Joseph who married Margaret Child in Watertown on 25 December 1701.

They had a daughter Hannah who was born on 20 March 1706/7 in Watertown.  This family is noted in Wyman & Bond.

There is also a connection between a Priest family of Weymouth and a son who moved to Salem and committed suicide there in 1664.