He was educated at Harrow School where he was in the cricket XI in 1852.
He was admitted at Trinity College, Cambridge on 5 January 1863. He played cricket for his college and also played for the Quidnuncs. In 1870, Moncreiff was awarded Bachelor and ordained a deacon at Lichfield when he became curate of Cubley, Derbyshire.
He was ordained priest in 1871 at Chichester.
He played cricket for various clubs and mainly for Gentlemen of counties including Derbyshire, Cheshire and Staffordshire. In 1873 he played one match for Derbyshire County Cricket Club when they needed 16 players in an extra match against Nottinghamshire.
He also played for Staffordshire and the Incogniti. In 1875 he became vicar of Clifton-upon-Teme, Worcestershire and played cricket regularly for Gentlemen of Worcestershire until 1881.
He became vicar of Tanworth-in-Arden, Warwickshire in 1885 and remained there until his death aged 69.
He was described as an eloquent preacher. Moncreiff married Florence Kate Fitzherbert, daughter of Colonel Richard Henry FitzHerbert, of Somersal Herbert on 4 January 1871.