The engraving is not great and certainly not official being likely engraved privately by a jeweller if done by the recipient, the medal roll does not record this medal as being named in any official way and was likely issued first as unnamed. The supposed recipient was the son of Sir Simeon Henry Stuart, 5th Baronet so likely had plenty of money for those fancy silver ribbon buckles and custom fitted leather case.
The only possible match would make it the group of Robert Charles William Stewart, later Lt-Colonel 72nd and 2nd Regiment, perhaps he preferred to use his middle name "Charles", he was a Captain since 1855 with the 71st Highland Light Infantry and was awarded the 5th Class Turkish Order of the Medjidie in the London Gazette, 2nd March 1858.
Obituary: Lieutenant-Colonel Charles Robert William Stuart, formerly a captain in the 2nd Queens Royal Regiment of Foot, died at Ottawa in Canada, on the 21st January 1883, in his 57th year. He was the Second Son of the late Sir Simeon Henry Stuart, Bart, of Harteley Mauduit, Hampshire, by his marriage, in 1815, with Georgina Frances, youngest Daughter of George Gun Esq, of Mount Kennedy, County Wicklow, and was born on the 27th October 1826. He was the last surviving brother of Sir Simeon Henry Stuart, the present and sixth Baronet, who was formerly a lieutenant in the Royal Canadian Rifles, Lt of the 71st Highlanders, and Captain in the 7th Lancashire Militia. His other brother Late Major Arthur John Stuart of the Royal Marines died earlier in 1868.
During the Crimean War he was rising up the ranks since joining the 71st as a young Ensign in 1846, promoted Lieutenant 1850, he was promoted to Captain without Purchase on 12th January 1855.
He appears to have moved to Canada to retire, he had served there with the 71st Foot previously circa 1850.