There is not a lot of information on Clan Muir
In doing a little research on the MUIR Clan I found these Clan members that supported Prince Charles
Here is all Muir Clan Names that I could find using the book
No Quarter Given: The Muster Roll of Prince Charles Edward Stuart's Army, 1745-46 (Paperback)
This book gives a list of those members of Bonnie Prince Charlie’s Army that were known to be killed, captured, deported or escaped after his defeat.

It also provides a little history on each of the units that were raised in his support

I offer this list to all of us that share a tie to Clan Muir

William Mair ,Ensign,Bannerman of Elsick’s

William Moore Cornet Fitzjames Horse

Robert Muir ,Ensign Hussars

William Moar/Moor Horse-hirer Kilmarnocks Horse and also Ogivy’s

Charles Moir Ships Master Stonywoods

John Moir Earl of Cromarties

Kenneth Moir Earl of Cromarties

Evav Moore Lady Mackintosh’s

James Moir , Lt. Colonel ,Stoneywoods

William Moir Lieutenant Brother to Invernenty ,Pitsligo’s Horses

Peter Sailor Lieutenant (Cousin to Moir )Of stoneywood Pitsligo’s Horses

William Moir Lieutenant (deputy Gov. of Aberdeen) Pitsligo’s Horses