Pullen was Anglican bishop of Cloyne and of Dromore, born at Middleham, Yorkshire in 1648, was, according to Cotton, grandson of Samuel Pullein (1598–1667), archbishop of Tuam.
When a bill "for ease to Dissenters" was introduced by the Earl of Drogheda in the Irish House of Lords on 24 September 1695, Pullen was one of the twenty-one bishops (out of forty-three peers) by whose votes the measure was defeated.
In 1697, Pullen (again anonymously) published "A Defence of" his position, and suggested that presbyterians before coming to Ireland should undergo a quarantine (in the shape of tests), like persons from a country infected with the plague.
The youngest, Joshua, born in 1687, entered Trinity College, Dublin, on 11 June 1701, graduated M.A., and was chancellor of the diocese of Dromore from 1727 until his death in 1767.
Besides two sermons and the pamphlets already noticed, Pullen is said to be the author of a scarce tract, "A Vindication of Sir Robert King's Designs and Actions in relation to the late and present Lord Kingston," 1699, no printer's name or place.