[1] He and older brother Nathaniel trained as clockmakers but both ran away from home and travelled for over two years in Wales and the west of England with a troupe of Gypsies.
About 1781 they settled in London where Andrew took up work as a manservant to Richard Cosway, who later trained him in portrait painting.
His brother Nathaniel Plimer also became a pupil of Cosway and a painter of miniatures.
[1] Plimer married on 21 February 1801, Joanna Louisa, daughter of John and Frances Knight of Wicken, Northamptonshire.
[1] His wife's younger sister Mary Ann Knight, another miniaturist, was a pupil and friend of Plimer.