The earliest manifestation of this root was unglossed ᴱ√TARA⁽⁾ in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. taru “horn” and ᴱQ. tarukko “bull” (QL/89). It was originally given as ᴱ√TAŘA “chevaux de frise [fortifications of wooden spikes]”, but that sense and associated derivatives (“hedge” words) were transferred to ᴱ√TAÐA; see that entry for details. As for ᴱ√TARA² “✱horn”, it also had derivatives in the contemporaneous Gnomish Lexicon such as G. târ “a horn” and G. tarog “ox” (GL/69).
The root ᴹ√TARAK “horn (of animals)” appeared in The Etymologies of the 1930s with derivatives ᴹQ. tarka/N. tarag of the same meaning, but the Noldorin word was also used of mountains, as seen in the name N. Taragaer “Ruddihorn” (Ety/TARÁK). The latter was an early precursor to the name S. Caradhras “Redhorn” in Lord of the Rings drafts of the 1940s; Taragaer was eventually abandoned (RS/419, 433).
An unglossed root in The Etymologies of the 1930s with derivatives like ᴹQ. tarya/N. tara “tough, stiff” and N. tarlanc “stiff-necked, obstinate” (Ety/TÁRAG). As pointed out by Christopher Tolkien, this last word is undoubtedly connected to S. tarlang in Tarlang’s Neck (LotR/790), which elsewhere was glossed “stiff-neck(ed)” (PE17/92, 98). In rough notes for Tolkien’s 1967 discussion of the Nomenclature of the Lord of the Rings, Tolkien indicated the initial element of this name was S. tarch, perhaps representing a shift of this root to ✱√TARAK (RC/536).
Neo-Eldarin: For purposes of Neo-Eldarin, I’d stick with the better-known earlier form of this root: ᴹ√TARAG.