Hello and welcome to Rootschat Squire

You may find some useful links and bits of info on the Royal Regiment of Foot, later 1st (Royal) Regiment, later Royal Scots here
www.rootschat.com/links/01gi9/ List of name changes around the time you are interested in which may help you sift through the confusion of various titles...
1684.05.01 His Majesty's Royal Regiment of Foot also known until 1751 by the names of colonels
1747. ranked as 1st Foot
1751.07.01 1st (Royal) Regiment of Foot
1812.02.11 1st Regiment of Foot (Royal Scots)
1821.08.29 1st, or The Royal Regiment of Foot
1871.12.15 1st, or The Royal Scots Regiment
1881.07.01 The Royal Scots (Lothian Regiment)
reorganised as the county regiment of Edinburgh (Midlothian), Haddingtonshire (East Lothian), Linlithgow (West Lothian), and Berwickshire, encompassing also its Militia and infantry volunteers
1887.05.01 Berwickshire transferred to King's Own Scottish Borderers district
1921.01.01 The Royal Scots (The Royal Regiment)
If you scroll down to list if colonols it does show Gen. Hon. James St. Clair (Lord Sinclair) as Colonol
27 June 1737 to 16 or 17 December 1762
It also lists movements for the battalions (see links under where it says "regulars"
1st were in England in 1748 and the 2nd were in Flanders.
Also links to books, archives, battles etc. You won't find his name listed but good background info
Milly