Graves, a member of the Royal Irish Academy, was chosen as Archbishop King's lecturer in 1799, and again in 1805. Also in 1799, he was made Professor of Oratory, in 1809 Regius Professor of Laws; in 1810 Regius Professor of Greek; and in 1806 and 1807 he held the office of University librarian. In 1814, he was appointed deputy professor of divinity, and in 1819 he succeeded his father-in-law as professor of divinity, a position he held until his death. In 1808, he had moved the College to include scripture as mandatory for all students as part of their academic instruction, and he succeeded in effecting some considerable improvements in the divinity school over which he presided from 1819.