This root has a lengthy history in Tolkien’s writing. It first appeared as ᴱ√HIL, unglossed but with derivatives having to do with children and offspring (QL/40); in this sense it may have reemerged later as the root √KHIN “child” (PE17/157; WJ/403). In the Gnomish Lexicon of the 1910s, the root appeared as χili with derivatives like G. hiltha “youth”, G. hilwed “adolescent”, G. hilm “posterity”, and G. hilmir “heir” (GL/49); the words for “heir” were also based on √KHIL in Tolkien’s later writing.
The root reappeared in The Etymologies of the 1930s as ᴹ√KHIL “follow”, its most notable derivative being ᴹQ. Hildi “followers, mortal men” as the second (following) race that were the children of Eru (Ety/KHIL). In later writings this name for Men became Q. Hildor “Followers” (S/103). The root √KHIL “follow” continued to appear in Tolkien’s later writings (PE17/18, 101, 157; WJ/387).
In The Etymologies ᴹ√KHIL had no Noldorin derivatives, and in the Quendi and Eldar essay from 1959-60 Tolkien said “the stem ✱KHILI ‘follow’ was not current in Sindarin” (WJ/387). Elsewhere, however, it is clearly evident as the basis for several Sindarin words, such as echil “follower(s)” (WJ/219) and Eluchíl “Thingol’s Heir” (S/188). It was also used with the sense “heir” in the phrase: Q. sinomë maruvan ar Hildinyar tenn’ Ambar-metta “in this place will I abide, and my heirs (hildë 1st-person-possessive plural), unto the ending of the world” (LotR/967), connecting back to its earliest meaning.
This root and ones like it were used for various spatial and temporal relationships during Tolkien’s life. Perhaps the earliest iteration in this chain of developments was the root ᴱ√PE “at, by” from the Qenya Lexicon of the 1910s, with derivatives like ᴱQ. penasta “being near at hand, support, backing” and ᴱQ. peanta- “give into one’s hands, give instructions to, enjoin” (QL/72). In Noldorin Word-lists from the 1920s Tolkien gave primitive ᴱ✶apa > ᴱN. ó “to, on” and ᴱT. pa, presumably of the same meaning (PE13/151). In a late note of unclear date Tolkien wrote:
> √apa “touch” (not with fingers but of the contact of surfaces, esp. vertical surface). So prep. apa, pa “touching, against”. In Q. this, espec. in form pā̆ is used as prep. = touching, as regards, concerning. Also the verb ape is used fig. as to touch one, concern, affect. In literal sense [touch] the strengthened weak verb appa is mostly used (VT44/26).
In another note from this period Tolkien glossed apa as “above but touching” (VT44/26).
At various points in the 1950s and 60s, apa- was given the temporal sense “after”, most notably in Q. Apanónar/S. Abonnen “After-born” (WJ/386-387), the former appearing in the published version of The Silmarillion (S/103). It was also used temporally in Q. apacenyë “of foresight” (MR/216). In a table of spatial and temporal roots from 1969, Tolkien gave √PĀ/PATA “after, behind of place” (PE22/147) and in another 1969 note Tolkien glossed apa, pā as both “before of time” and “after (later than)”, with both being deleted (VT44/36). Other similar roots in the semantic space of “after” include √EPE and √OPO.
Neo-Eldarin: As indicated by the discussion above, Tolkien’s treatment spatial and temporal prepositional elements was wildly inconsistent. √APA was one of the elements Tolkien used for “before” and “after”, but also as “on” or “touching”. For purposes of Neo-Eldarin, the most useful definition of √PĀ/APA is “touch”, for which we have no other good late roots, so I would assume this was its primary meaning. I generally prefer ✶epe for “after (of time); before (of space)” and ✶nō for its opposite. However, I think apa- might be a euphonic variant of epe-, perhaps limited to “after” of time, to justify Q. Apanónar/S. Abonnen “After-born”.