He was briefly Provost of Tuam and Chancellor of St Patrick's Cathedral, Dublin, before he was nominated the Bishop of Clonfert and Kilmacduagh on 14 May 1730 and consecrated on 7 June 1730.

Synge is particularly well known for his 221 letters to his daughter Alicia (1733-1807), the only survivor out of the six children of the Bishop and his wife Jane Curtis (d. 1737) whom he married in 1720.

There is almost no aspect of the young girl's life upon which her father did not comment including dress, health, diet, exercise and behaviour in social situations.

His principal concern was with her education generally and specifically her ability to write letters well; his advice to her on this score was to copy Swift for grammar and punctuation.

The bequest of these letters to Trinity College Library, University of Dublin, by Synge's descendant Marie-Louise Jenner, has revolutionised eighteenth-century Irish social and women's history.