In contemporary vernacular, 'hold your tongue' is equivalent to "Stint thy clep!". 'Clep' is a form of the obsolete noun 'clepe':
Forms: Also clep.
1. A call, cry, shout. rare.
OED, clepe, n.
And 'stint' is straightforward — it's not a rare form of a rare word, although it is archaic or dialectal in this transitive sense:
6. a. To discontinue (an action); to hold in check, restrain (one's own actions or organs of action). Now arch. and dial.
OED, stint, v.
As to "when and where these words are used in this way", OED's last attestion of 'stint' in sense 6a is
1881 S. Evans Evans's Leicestershire Words (new ed.) (at cited word) Yo' stent yer nize!
So, "where" is Leicestershire at least, and "stent yer nize!" is also the equivalent of 'hold your tongue' ("nize" = 'noise'). The "when" is 18th, 19th, and early 20th centuries (latterly).
For 'clep', OED is not so helpful, but an easy-to-find attestation is the below from The Tint Quey, 1796, by Richard Gall (emphasis in the following quote is mine).
Meg's passion like a rock took low:
"Whisht! haud y'er clep, an' speik nae langer,
"Ye ne'er-do-weel, to raise my anger —
Note that an errata printed on the page before the title page of The Tint Quey reads "In pages 1st and 13th, for 'Tint Quey' read 'Tint Cow'." My surmise is that the cow in question was older, or had a calf, but observe that 'quey' ("A heifer, a young cow, 'of any age up to three years or until she has had a calf'", quey n., The Scottish National Dictionary) appears on other pages of the poem than the first and thirteenth.
After finding the above attestation in the 1796 publication of The Tint Quey, ascribed in pencil on the title page to R. Gall, and said to be "In the Scottish Dialect", I took a cue from that and checked The Scottish National Dictionary for 'clep' and 'stint'. In SND the phrase "haud y'er clep" from Gall's poem (a later, 1819 edition) is used as attestation of a form of clype n.1, and is translated as "hold your tongue".
SND also give this definition of stent n.3, v.3 (sense II.2.):
2. tr. To confine, restrict, limit, check, curb (Sc. 1808 Jam.; Rxb. 1971); to scrimp, stint. Ppl.adj. stentit, delimited, definite.
Although 'stint' is not given as a variant form of stent n.3, v.3, and does not appear in the attestions for sense 2, that appears to be an oversight; 'stint' does appear in the attestations for another sense, and 'stent-stint' are mutually common variant spellings.
This attestation is given for sense II.2. of stent n.3, v.3:
Gsw. 1856 Deil's Hallowe'en 35:
Canna ye stent your gab a wee?
The particular collocation you encountered is almost certainly the creation of Patrick Rothfuss, playing on archaic uses and Scottish dialectal words and senses for dramatic effect.