Seems to have disappeared from the scene according to various sources.....
This from Imdb....
After two seasons, Squire went to the B.B.C. to make 'Paul Squire Esq.' which was absolutely ghastly, a pale imitation of the Mike Yarwood show. It flopped. He returned to I.T.V. in 1983 for one last series - screened at 5.15 P.M. on Mondays - and then it was goodbye forever from Paul Squire. He returned to the cabaret circuit.
He would not be the first comic to fail to find the right television format; Fogswell Flax and Jessica Martin also spring to mind. Despite his youth, Paul was perhaps a little too 'old school' at a time when British television comedy was in the midst of the alternative revolution, as epitomised by 'The Young Ones' and 'The Comic Strip Presents'.
Had Squire caught on, of course, its likely that he would have been extinguished in the same early '90's purge that rid the airwaves of Russ Abbot, Little & Large and Bobby Davro. We shall never know for sure. A shocking waste of talent, all the same