There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
hyar-
verb. to cleave, to cleave; [ᴱQ.] to plough
hyarya
adjective. left (hand)
A word appearing as {harya >>} hyarya “left” in The Etymologies of the 1930s under the root {ᴹ√KHAR >>} ᴹ√KHYAR (Ety/KHYAR). A prefixal form hyar- “left-hand” was mentioned in notes on The Feanorian Alphabet from the 1940s (PE22/51).
harmen
noun. south
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
A verb appearing as hyarin “I cleave” in The Etymologies of the 1930s as a derivative of from the root ᴹ√SYAD “shear through, cleave” (Ety/SYAD). In the Outline of Phonetic Development (OP1) from the 1940s, Tolkien had an (unglossed) verbal stem hyar- also derived from ᴹ√SYAD, but in that document the root seems to mean “compact, compress”. However in the Quenya Verbal System from 1948, hyare again meant “cleave” (PE22/102). See the entry on √SYAD for further vacillations on the meaning of the root.
Conceptual Development: The Gnomish Lexicon of the 1910s had ᴱQ. hyanda- as the cognate of G. †hanna- “mow, cleave” (GL/48) likely based on the early root ᴱ√HYAŘA “plough through” [HYAÐA] (QL/41). Early Qenya Word-lists of the 1920s had ᴱQ. hyar- “plough”, probably form the same root (PE16/144).
Neo-Quenya: For purposes of Neo-Quenya, I would keep the sense “cleave” for the basic verb despite Tolkien’s vacillations on the meaning of the root. I think it could also retain its 1920s meaning “plough” = “✱cleave the earth”.