Hi Diddy
The two references I have are:
Obituary of considerable Persons; with Biographical Anecdotes p 281 At Ipswich, in his 61st year, Wm. Clarke esq. many years a portman, and several times a chief magistrate, of that borough (Gentlemans Magazine March 1791)
Monthly Obituary for Feb and Mar 1791: William Clarke, esq, at Ipswich, many years Portman, and several times Chief Magistrate of that Borough (The European Magazine, and London Review, Volume 19)
I have since had 28 Feb 1791 offered as the date of death but this is from a biographical note concerning his wife Elizabeth and not specifically about William Clarke.
Regards
Tony Randall