Niblett was elected Warden (head) of All Souls College, Oxford in 1726, a post he held until 1766.
[1] During his time as Warden of All Souls College, he was also Vice-Chancellor of Oxford University from 1735 until 1738.
[2][3] A monument to Niblett and his wife Elizabeth was erected at All Souls College, Oxford in 1766, being sculpted by Nicholas Read.
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