The Quenya future tense refers to events occurring in the future: i atan matuva, matuvan “the man will eat, I will eat”. The English future tense uses a helping verb “will”, but the Quenya future tense has its own conjugation, with the suffix -uva.

Origins of the Future Tense: Tolkien discussed the origins of the future tense in a number of places. Unlike the other verb tenses, the Quenya future did not originate in Common Eldarin (CE), as described in Common Eldarin: Verb Structure (EVS2) from the early 1950s:

Future. All the Eldarin languages express, or in their older periods expressed, a simple future inflexionally, but the inflexions and patterns are different in each. It is thus probable that the development had not been completed at the time of the separation of the branches. In CE the future could still be expressed evidently by the aorist with defining adverbs (see above), and some of the habitual collocations were already hardening into fixed agglutinated groups on the way to becoming inflexional; while there were also probably some verbal expressions, like English “will go, am going to say” (PE22/131).

A similar statement appears in Quendian & Common Eldarin Verbal Structure (EVS1) from the late 1940s:

Future. All the Eldarin languages express a simple future inflexionally, but the inflexions and patterns used are different. This may mean that the device of an inflexional future had already been achieved in CE but that the later languages all abandoned the older pattern and separately substituted new ones; or that the future could still in CE be expressed by the aorist with defining adverbs, while there were already a good many other modes of expression in competitive existence among which the later languages chose different modes to become their normal pattern. Cf. English “I go home (soon, tomorrow, next year)”; or defined by a future sentence: “I shall go, when he calls”; beside “I shall go, will go, am about to go, am going to go etc.” (PE22/131).

Tolkien went on to describe the Quenya future formation in EVS2, as a derivative of the root √UB:

In Quenya the adverbial phrases did not harden into inflexional forms, but in older Quenya the aorist could be used with similar adverbs (en, enya) in a future sense: as AQ en i matinye “I shall eat then, soon”. The usual formation is with uva, often added to the bare stem: matuvanye “I shall eat”; but this was used far more constantly than the original CE matubāni, and had become an undefined future without implications of nearness or remoteness.

[The last refers to a separate statement about CE in the same document: “by adding ubā to the bare verbal stem as matubāni ‘I shall eat’, the remoter future”. The “remoter future” aspect of -ubā was lost in Quenya.]

The “suffix” in this case was -ubā, and the u had no connexion with the u-vowel seen after the stem in a number of old verbs [u-verbs] (see below). √UB was in fact a verbal element with the sense “ponder, have in mind”, and the form ubā is a 'present' formation of the type melā described above [a-verb]. Thus Prim. N. and Q mat-ubā-ni/nje signified “I intend to eat”. The stem ub, uv no longer survives in recorded Quenya as a separate verb; but cf. Q úvie “pondering, consideration”; ON ūba- “ponder, make up one’s mind” (PE22/131-132).

Tolkien returned to the topic of the future in Late Notes on Verb Structure (LVS) from 1969:

Q. developed a pure future of fact or eventuality, with a stem ubā suffixed to the bare base (without ómataima): as *karubā- “will do, is going to do”. This base UB provided a verbal stem (an a-verb) uba- in original sense: “impend, be imminent, approach, draw near”. In this form it was at an early date affixed to the simple verbal stem, but with a weakened and generalized sense: as e.g. *kar/ubā/ni = “I draw near to doing, I am about to do (it)” > CQ [here “Classical Quenya” = Parmaquesta, PQ] caruvan(ye) “I am going to do/shall do (it)”. The sense of imminence was lost; and no special sense of unwelcome approach was developed, such as appeared in Q. partly perhaps owing to influence of the “bad” sense of ū-prefix, and its derivatives.

As an independent word the verb uba was lost. But a strengthened form ūva was used “impend, be imminent” nearly always in a bad sense: “threaten (to come)”. Thus ulo ūva “rain (unwelcome) is coming/threatens”; but uluva “it is going to rain, it will rain”; hríve ūva vēna “winter is drawing near (to us)”, which would not be said of laire “summer” — unless for some special reason its approach was unwelcome (PE22/167-168).

Thus in the 1960s, the phonetic origins of the future suffix -uva remained the same, but its CE sense was altered from a remote future to a near future, and the meaning of the root √UB was revised from “ponder” to “approach, draw near”.

Forming the Future: The formation of the future is fairly straightforward: simply add the suffix -uva to the verb stem, replacing the final vowel if there is one: mat- “eat” → matuva (PE22/162); orya- “rise” → oryuva (PE22/157, 164). There are only a few exceptions to this rule:

• The u-verbs lengthened their final -u in the future tense: [ᴹQ.] liru- “sing (gaily)” → lirúva (PE22/117).
• The basic verbs with stem ending in -v (from both ancient w or b) lose this consonant: tyav- “taste” → tyauva (PE22/152). For verbs with uv in the stem, the result was: tuv- “discover” → †tuvuva > túva > tuvua, because otherwise the future would be identical to the present (PE22/155).
• For tā-causatives and (rare) yā-causatives, the final -a of the stem was not lost: orta- “raise” → ortauva (PE22/159, 164); tulya- “lead” → tulyauva.

In the case of u-verbs, the only examples we have are from the Quenya Verbal System (QVS) of the late 1940s, but the pattern remains phonologically sound in the systems of Tolkien’s later writings.

Conceptual Development: The Quenya future was established very early in Tolkien’s writing. In The Qenya Verb Forms of the 1910s, the future suffix was -va: ᴱQ. tul- → tulva (PE14/28, 31), but he also said: “Ending of future is -uva- in many verbs, -ta derivatives and long stem cons[onant] verbs, as hosta-, hostuva; karpi-, karpuva” (PE14/34).

In the Early Qenya Grammar (EQG) of the 1920s, Tolkien decided the -uva suffix was also used for basic verbs. He said: “The future stem is obtained by the suffix -(u)va” (PE14/56). Examples in EQG include: tule → tuluva, tanga → tangauva, tantilta → [tantil]tŭva, tulya → tulyuva, lapta → laptuva, kelu → kelūva, lokta → lokatwa (PE14/57-58). The last example is the only one with suffixal -va > -wa instead of -uva.

The suffix -uva was still used in the Qenya Conjugations of the late 1920s or early 1930s, where it also served as the suffix for the conditional tense, distinguished from the future by its use of the short vs. long pronominal suffixes: 1st person conditional tuluvan vs. future tuluvanye, 2nd person conditional tuluval vs. future tuluvaste, etc. (PE16/124-127). Futures in contemporaneous poems like ᴱQ. Oilima Markirya used uva-futures as well, such as ᴱQ. kiluva “shall see” (MC/213), which became kenuva in the 1960s version of the poem (MC/221).

In the Quenya Verbal System (QVS) of the late 1940s, the -uva suffix continued its use in basic verbs, and the tă- and yă-formative verbs used -uva with replacement of the final -a: ᴹQ. nahta → nahtuva, sirya → siryuva (PE22/115). However, many other derived verbs in QVS used only -va, along with lengthening of the final -a: ᴹQ. faráva “will hunt”, hopáva “will wait”, oláva “will grow” (PE22/116), ortáva “will raise” (PE22/104). This va-future formation is seen in the late 1930s poem Fíriel’s Song: ᴹQ. antáva “will give” (LR/72). As Tolkien described it in QVS:

The Future. In Quenya this was made with the suffix -vā. The simple future: this showed -va added to the base + u. On the origin of the vowel [u] see above. It always in Q. appeared before -va in strong verbs, when added to the aorist base. Also in words with present-aorist formatives: as ista “know”, istuva “shall know”. Those with suffix -u already as liru­ “sing” usually show lirúva (-ūva). The u is absent when -vā is added to stems already ending in an original long vowel: so ortuva “will rise”, ortáva “will raise” (PE22/104).

In Quendian & Common Eldarin Verbal Structure (EVS1) written shortly before QVS, Tolkien described a distinct CE origin for the future:

In Quenya the suffix is -bā (Quenya -vā̆-), which is preceded by u (in case of most verbs). The origin of this formation is not clear; but bā is certainly verbal, not adverbial. Cf. √BĀ-, BANA “go, proceed”, as seen in Quenya vanwa “gone, over”. Q karuvā- “will make” thus originally = “is proceeding to / going to / make” (PE22/97).

In Common Eldarin: Verb Structure (EVS2) from the early 1950s, the origin was revised to the root √UB as described above (PE22/131), and thereafter future suffix -uva was used with all verb classes.

Neo-Quenya: For Neo-Quenya, I think you can just use -uva with all verbs, replacing the final vowel, with the possible exception of causative verbs which should use -auva.