He features in a group portrait, by Johann Zoffany, of the founders, and is one of three sitters (with Francesco Bartolozzi and Giovanni Battista Cipriani) in a 1777 portrait displayed in the National Portrait Gallery in London. He was Keeper of the Royal Academy from 1783 until his death in 1790. He exhibited a portrait in oil in 1776.
He worked, with fellow Italian sculptor Giuseppe Ceracchi at Somerset House, and on statues at Custom House in Dublin. He is particularly noted for various church monuments, including a memorial to Lady Sophia Petty at All Saints' Parish Church, High Wycombe, Buckinghamshire, and one commissioned by Joseph Damer in 1775 to commemorate his wife Caroline, which stands in the north transept of Milton Abbey in Dorset.
Also in 1775, Carlini was commissioned by Dr William Hunter, first Professor of Anatomy at the Royal Academy schools, to make a cast of the flayed corpse of a recently executed smuggler. The figure was posed as a Roman statue, the "Dying Gaul", and given the pseudo-classical title "Smugglerius".
He died unmarried at Carlisle Street, London, leaving all his estate to "Elizabeth Watton, spinster", his maid and housekeeper.