The verb ᴱQ. nesta- “feed” appeared in the Qenya Lexicon of the 1910s as a derivative of the early root ᴱ√NESE “give to feed; feed, pasture; graze” (QL/66). It has past forms nēse and nesse, indicating a close relationship to the verb ᴱQ. nese- “graze, pasture, give to feed, feed” from the same root, which likely would have had the same or similar past-tense forms.
Neo-Quenya: For purposes of Neo-Quenya, I would combine both these early verbs into ᴺQ. nesta- “to graze, pasture, give to feed, feed”, derived from the Neo-Root ᴺ√NES.
The noun ᴱQ. nesta “(act of) feeding” appeared in the Qenya Lexicon of the 1910s derived from the early root ᴱ√NESE (QL/66).
Neo-Quenya: For purposes of Neo-Quenya, I’d instead use the gerund ᴺQ. nestië of the verb ᴺQ. nesta- “(give to) feed”.