Pronounced as English “w”. It appears most frequently following another consonant, such as in curwë “skill” or tengwa “letter”. That’s because in Quenya’s phonetic history, initial and intervocalic w became v (PE19/72) as in vinya “new” < √WIN or céva “fresh” < ✶kēwā, while between a vowel and a consonant w became u̯ and formed a diphthong (PE19/100) as in laurë “gold (light)” < ✶glaw(a)re.

Despite these phonetic rules, initial w does appear in some Quenya words, such as wendë “maiden” and wilwarin “butterfly”. These surviving initial w may be the result of more ancient initial gw-, the clearest example of this being words like walmë “excitement” < √GWAL. Here the initial g weakened to the voiced velar spirant ʒ before ultimately vanishing, but it survived long enough to prevent the w becoming v, at least in Classical Quenya. Tolkien did say that these initial w from gw also eventually became v, but later than isolated primitive w:

gw became [ʒw], and then initially a spirantal frictional w (with slight friction both at the back and at the lips); but already in PQ this w was weakened. The weakening was later than the beginnings of the change of original w > v, and w < gw remained as such and distinct from w, v for some time: in earlier PQ it is not represented by the sign for v; but in TQ it had become identified with w, v (PE19/75-76).

Given the statement that “in TQ it [w from gw] had become identified with w, v”, Neo-Quenya writers often change all initial w to v, for example writing vilvarin “butterfly” or vende “maiden”, something Tolkien himself did on occasion. Entries in the Eldamo lexicon represents w- words with v-, though it indicates the older pronunciation with a following [w] in brackets. Tolkien’s use of initial w could instead represent either archaic or dialectical pronunciation.

There are also some ambiguities in the pronunciation of w after another consonant. The letters w and y are unique in that they represent the only consonants that can make up three-consonant clusters in Quenya such as ngw or nty (PE19/82). Furthermore, consonants pairs ending in w or y were the only pairs that allowed a preceding long vowel or diphthong, such as sáque/saique or mátya/maitya, and (mostly) the only pairs allowed at the beginning of words. They were also “short enough” to allow for the Quenya syncope: [ᴹQ.] salquë “grass” < ✶salakwē.

As such, it is possible this following w represents a labialization of the preceding consonant, so that ngw = [ŋgʷ] and qu = [kʷ], and many Neo-Quenya writers assume that such sounds are unitary consonants. However, in notes on Qenya Spelling from the late 1930s Tolkien said:

q, ngw [= ŋw] are not actually strictly simple consonants in pronunciation though they can stand initially where Qenya does not tolerate actual consonant groups ... q (kw) consists of a lip-rounded k̊ followed by a partly unvoiced w-offglide (more marked medially than initially) ... gw which only occurs in the medial group ngw is the voiced counterpart: a lip-rounded g̊ followed by a w-offglide (PE22/65-66).

According to this, qu and ngw are actually pronounced as full clusters [kw] and [ŋgw] (more accurately [kʷw̥, ŋgʷw]). It thus seems likely that clusters with w and y were considered “long enough” to attract stress, so that [ᴹQ.] ataquë “building” was stressed on the second syllable rather than the first. I think it is best to think of qu and ty as “semi-clusters”, somewhere between a consonant pair and a labialized or palatalized unitary consonant.