In Ancient Quenya any r following a voiceless stop or aspirate developed into s, a sound change with nearly identical descriptions in both the Outline of Phonetic Development (OP1) from the 1940s and the Outline of Phonology (OP2) from the 1950s:

The vocalic element was not however developed before r at an early period. In Q. [r] before or after other consonants other than [r], was weaker than in isolation, and was in such cases only slightly trilled. Consequently when unvoiced, as after p, ph; t, th; k, kh, [r] became evidently in AQ a voiceless, probably untrilled, ř. This was transformed into s prehistorically - before the spirantalization of aspirates, so that the original products of say pr, phr were alike ps, identical with the products of p, ph + ancient s (OP1: PE19/39-40).

At this (prehistoric) period r did not become syllabic, possibly because it was early more susceptible of unvoicing than l. In Q. r before or after other consonants (other than r itself) was weaker than r in isolation, and in such cases only lightly trilled. When unvoiced it became a frictional ř which was soon transformed into s. This development occurred prehistorically & before the spirantalization of ph, th, kh; so that the most ancient products of both thr and tr, for instance, were ts, identical with the products of CE th + s and t + s (OP2: PE19/83).

Tolkien also mentioned this sound change in other contexts elsewhere in OP1 (PE19/43-44, 47) and OP2 (PE19/86, 88), under his discussion of the medial phonetic developments of voiceless stops and aspirates. This change of r to s was very ancient, before the spirantalization of aspirates, as noted above. Specific examples of this sound change are hard to find, however, since in many cases the consonants had already been inverted due to various Quenya metatheses. However, there are at least a couple words that seem to demonstrate this change:

• ᴹ✶mitra > ᴹQ. mitsa “small” (EtyAC/MIT), from a deleted root.
• ✶mikrā > Q. mixa [miksa] “sharp-pointed” (WJ/337).
• ✶NEK¹ [+ rā] > Q. nexa [neksa] “sharp, angular” (PE17/55).

Christopher Tolkien wrote the second example as miχa with Greek χ, but I think it is very unlikely that kr would have become a voiceless velar spirant, and that x [ks] is more likely to be what Tolkien intended. The third example nexa was pointed out by Raccoon in a Discord chat; compare it to its variant form nerca with metathesis.

Conceptual Development: This sound change was not mentioned for either voiceless stops or voiceless spirants in the early Qenya Phonology from the 1910s, and indeed it seems r after voiceless stops (in cases where the combination did not undergo metathesis) became syllabic and developed some kind of vowel, usually a: pr, tr, kr > par, tar, kar (PE12/22-23).