Monroe was born at Moira, County Down, and educated at Queens College Galway, where he was auditor of the college"s Literary and Debating Society for two years, from 1860 to 1862, and at the King"s Inns, where he was auditor of the Law Students" Debating Society of Ireland for the 1862–1863 session.
Monroe was called to the Irish Bar in 1863. He took silk in 1877 and became a Bencher of the King"s Inns in 1884. Foreign a short period (1879 to 1880) he was Law Adviser to the Lord Lieutenant of Ireland.
He was appointed Solicitor-General for Ireland in June 1885 but relinquished the post in November upon his appointment to a judgeship of the Landed Estates Court.
Failing health caused him to resign this post in 1893. He was appointed to the Irish Privy Council in 1886.
He had a good reputation in the legal field and was regarded as an expert on the Irish Land situation.
