Quick service record of the 21st Light Dragoons:
Ireland from 1803 to 10 April 1804
England: arrived: April 1804; departed at Portsmouth: 16 May 1806
Cape of Good Hope: arrived: 6 August 1806; departed 27 August 1806
2 troops went to South America: arrived at Monte Video 16 January 1807; departed 28 July 1807
2 troops returned to Cape of Good Hope on 5 September 1807
The regiment left for Bengal on 18 and 19 July 1817 and arrived thre on 10 Sept 1817
Departed for England in October and November 1819; arrived at Gravesend on 13 April and 31 May.
Disbanded at Chatham in May and June 1820
(This is all from WO 380/2 in the National Archives).
You can find out if any officer was actually with the regiment through WO 17:
Before 1813: WO 17/48
https://discovery.nationalarchives.gov.uk/browse/r/h/C600925After 1813 it would need going through each year's box to find the 21st Light Dragoons
https://discovery.nationalarchives.gov.uk/browse/r/h/C89834