Background The 75th (Stirlingshire) Regiment of Foot (later the Gordon Highlanders) was a single battalion regiment. It had previously been in India, but when it was due to come home in 1806, so many men elected to leave the Regiment and settle in India, that the regiment was little more than a cadre on its return to Britain. In view of this, on 7 April 1809 it lost its highland status, meaning that the men no longer wore the kilt or other accouterments of highland dress. At that point it was officially retitled as the 75th Regiment of Foot, although it was still known colloquially as the Stirlingshires.
However the Napoleonic wars were still going on, and the Army was short of men. So after a big recruiting drive in Scotland, Ireland and later, England, the Regiment appears to have been back up to something approaching full strength, although very inexperienced. After a stay in the Channel Islands in 1811, it was sent to the Mediterranean. It then served in the following places:
1814 Ionian Islands
1821 Gibraltar
1823 England
1824 Ireland
1830 England
1830 Cape of Good Hope
1827 So it looks like the Regiment would have been recruiting in Ireland in 1827-8. Because Ireland was classed as a home posting, the Regiment wouldn't have had a depot located elsewhere in Britain. To get more precise locations for where they were in Ireland, you would need to look at the muster and pay rolls held in the National Archives. That would require a personal visit, as they haven't been digitised.
If going to Kew is not an option, you could try contacting the
Gordon Highlanders Museum to see if they either have copies of the muster rolls or have other information about the places where the Regiment was stationed. Usually, Regiments in Ireland were split up into a number of garrisons within a province or one of the ancient kingdoms, each manned by one or more companies.
More general information see
Here and
Here