OS. final [e] became [a] after single [s] and [st]; [-se|-ste|-sse] > [-sa|-sta|-sse]
In the Old Noldorin of the 1930s, it seems a final [e] following an [s] or [st] shifted to [a], unless it followed a double [ss], in which case the [e] was preserved. The clearest examples of this rule are ᴹ✶khyelesē > khelesa > ON. kheleha (Ety/KHYEL(ES)) and ᴹ✶peltakse > ON. pelthaksa (Ety/PEL). In the case of [st], note that ON. phasta has the cognate ᴹQ. fasse (Ety/PHAS), which implies a primitive form ending in [e] and thus a similar change of [e] to [a] in Old Noldorin after [st].
For counter-examples involving [ss], consider ON. (s)pharasse in which the final [e] is preserved, and similarly for its (rejected) precursor pharasse (Ety/SPAR, EtyAC/PHAR²).
Since later in Noldorin, short final vowels vanished, in many cases this phonetic change in Old Noldorin is not noticeable; whether the final vowel was -e or -a before it vanished has little effect. In a few cases, though, this change to -a in Old Noldorin can have further ramifications, in particular via a-affection, whereby short [i], [u] became [e], [o] preceding final [a].
There are only two attested examples of primitive forms ending in -se where the a-affection may also apply. The first example is ᴹ✶tupsē > N. taus (Ety/TUP). Here, the ON. shift to final -a means that the medial vowel [u] became [o], which means that after the voiceless stop was spirantalized and then vocalized before the [s], it produces the same final result as [o] in this position: the diphthong [au]. Compare this example to ᴹ✶oktā > N. auth (Ety/KOT).
Conversely, consider ᴹ✶tyulussē > N. tulus (Ety/TYUL). In this case, since the [u] remains, it implies that a-affection did not occur, indicating that the final -e was preserved after the double [ss], as noted above.
Conceptual Development: It’s not clear whether this sound change still applied to Sindarin, but there is nothing to contradict it. There are no evidence (for or against) for this change in Tolkien’s early versions of the language either.