Shippen acted as a tutor at Brasenose College, Oxford was awarded a Master of Arts degree on 4 July 1699.
Shippen was elected Principal (head) of Brasenose College, Oxford in 1710 and attained a Doctor of Divinity.
[4][5] In 1710, the same year he became Principal of Brasenose, he married Frances (died 1728), daughter of Richard Legh of Lyme Park, and widow of Sir Gilbert Clerke of Chilcote.
Following this, on 3 October 1710 he resigned his professorship at Gresham College in favour of his elder brother, Edward Shippen (1671–1724), who had graduated from Brasenose with an M.A.
Robert Shippen was buried in the chapel at Brasenose College, where he is commemorated with an epitaph (by Dr Frewin) and a bust.