There have been a number of British cavalry regiments with the number 19. The one you are interested in is 19th Regiment of (Light) Dragoons which dates from 26 April 1786. It took the title 19th Regiment of (Light) Dragoons (Lancers) on 3 September 1816. It was disbanded on 10 September 1821.
The modern successor regiment was 15th/19th The King's Royal Hussars which amalgamated with 13th/18th Royal Hussars in 1992 to form a new regiment called The Light Dragoons.
During the period the regiment, or elements, served in India from 1803-1806, UK 1807-1811, America 1812-1815.
JC