The word empollie appeared in the untranslated phrase á rike empollie in rough notes from the 1960s (PE17/167). Christopher Gilson suggested this was likely an early attempt by Tolkien to define the Quenya expression for “try harder”, elsewhere given as ā rike am(a)ríkie which more literally means “try [with] more trying” (PE17/94). The second element of empollië is clearly based on pol- “to be [physically] able to” and Arael suggested its first element might be en- “again”. If so, it may mean something like “✱[with] retrying, redoing”.
Neo-Quenya: I would avoid empollië in the sense “harder” for purposes of Neo-Quenya, using the á ricë amrícië construction instead; see that entry for discussion. However, empollië might be worth retaining in the sense “✱retrying, redoing, another attempt”. I also think it is worth adapting an intensified form of this noun as ᴺQ. ampollië meaning “great effort, struggle”.
Tolkien used this root as the basis for Elvish “to be” verbs for much of his life. ᴱ√NĀ “be, exist” first appeared in the Qenya Lexicon of the 1910s with derivatives like the verb ᴱQ. ná- “to be” and ᴱQ. nasta “existence, being, creature” (QL/64). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. na- “to be” and G. nast “being” (GL/58-59). It appeared again in The Etymologies of the 1930s as ᴹ√NĀ “be” (Ety/N²), along with an invertible variant ᴹ√ANA² “be, exist” with the derivative ᴹQ. anwa “true, real, actual” (Ety/ANA²); this seems to be the only point where Tolkien considered this root to be invertible. The root √NĀ “be” is mentioned several times in Tolkien’s later writings as well (PE17/93; PE22/147; VT49/27-28).
The root √NĀ was often contrasted with other roots of similar meanings. For example:
> Stem of verb “exist” (have being in primary world of history) was √EŊE, distinct from √NA joining adjs./nouns/pronouns in statements (or wishes) asserting (or desiring) a thing to have a certain quality, or to be the same as another (PE22/147).
There were also periods when roots other than √NĀ were the basis for “to be” statement in Elvish. See the entry on √EÑ “exist” for a conceptual history of these alternate roots and their derivatives.