The word G. hai “in good time, punctually, early” appeared in the Gnomish Lexicon of the 1910s, with an adjectival variant G. hair “timely, punctual, in good time” which in turn had its own adverbial variant haidra of the same meaning (GL/47). The derivation of these words is unclear.

Neo-Sindarin: There aren’t any Sindarin words for “early” in Tolkien’s later writings, so I’d retain ᴺS. hai as neologism for “in good time, early, punctual(ly)” function as both adjective and adverb. I would assume it is related to S. hí “now”, derived from primitive *khiyā. Compare ᴹ✶miniı̯a > [N.] minei “single, unique” [ᴺS. minai].