The pedigree in John Hutchin's, The History and antiquities of the county of Dorset, vol. 1, p. 347 does have that he died in 1696, with over the page his burial in that year at Compton Valence, Dorset. His son also called Thomas Pelham, was the Rector at Compton Valence and died in 1690.
TheGenealogist website does have transcriptions of Thomas Pelham, buried at Compton Valence on 2 June 1690 and another Thomas Pelham buried same place on 26 June 1696, without any other information that might help to identify who was who. Maybe the original parish registers might have more detail, if they can be found?
For some reason on his profile we have born after 1594 but his birth at Chichester on 23 Jan 1597/8 is in the biography, though I notice this date comes from a secondary source with no citation to any primary source.
It would be unusual but not impossible for him to be close to 100 years old when he died.