If he was in the Grenadier Guards you have a better chance of finding his record than if he was in a line infantry regiment. This because when a soldier completed less than his commitment (in the middle of the nineteenth century this would have been for 12 years) and he wasn't seriously injured, he didn't qualify for a pension, so his record would have been destroyed at some point after he had left the service. However the Brigade of Guards (which included the Grenadiers) maintained their own records and these were generally preserved. Not all records have survived, but a much larger proportion still exist than is the case for the rest of the Army.
If you have a subscription to FindMyPast, I would start there, using their Grenadier Guards 1656 - 1874 collection. If you don't, try searching in WO 437 via the [UK] National Archives website:
https://discovery.nationalarchives.gov.uk/details/r/C17859050I'm not sure if Ancestry also have this record set.
