I've never come across 'carrier' meaning a law officer before. Neither have Chambers Dictionary, Chambers Scots Dictionary, various online glossaries of Scottish legal terms, the Oxford English Dictionary, or Jamieson's Etymological Dictionary of the Scottish Language Online.
What is your source for that information?
Nor me Forfarian.
All these years I just thought he was a man with a cart.

If you follow what Stob Ban has said, and put Carrier in Scotland 1751 into Google, it indeed comes up with a link to wikipedia, and gives the headings, 'Judiciary, lawers, advocates' etc as they have obviously seen.
Clicking on that, brings up a page on wikipedia about Scotland in 1751, with paragraph headings - "Judiciary, lawyers, advocates' etc. Nowhere does it mention carriers. I suspect Google has just brought up the last bit of the search terms.
The pitfalls of taking information from a Google search I fear.
Unfortunately, it does mean that inferences may be drawn from what you see that may well be erroneous.
Until I get positive proof that a carrier was anything more than a person who moved goods from one place to another, I'm sticking with that.