ANALYSIS (And partial incomplete answer)
Let me spell this out for you
and see what you can do.
I begin by being half full
FU (LL) - we use FU since having LL at the start of a word doesn't make sense. Option 2: we use the COMP part of "complete" since complete is a synonym for "full"
Then onto you, don't be dull
onto you likely means the letter "U", or it can be "on two u" signifying a second "U" in the word
I'm around for a third of a year
This is likely to be the synonym "annual" or "annum", but only "annual" divides nicely into thirds, so it could be either an, nu, or al. It can also be interpreted as "twelve months", which gives us several possibilities: 1) take a part of "twelve months" and use that; 2) the total number of T and E's make up a third of the phrase "twelve months"; 3) A third of twelve months is 4 months. Usage of the phrase "four" or "triannual" or "Quadrimestrical" or "quad" is possible.
Finally, without me, there is no gear
Either signifying one of the letters (G or R, likely) in gear - the other option here would be that if the hint was something to do with gears (either in a car, or in machines (cogs and gears)).
Taking into account the hint that the answer is shorter than "short", which is 5 letters, the answer should be 4 characters or less. This means that because there are 4 clues, it's likely that each clue represents a single letter.
Half full - half the letters in full are L's, so we start with the letter L.
Onto you - Letter U
At this point we can start looking at this: http://www.wordhippo.com/what-is/starting-with/4-letter-words-lu.html
year, aka annual - it's the third letter, so a third of a year makes sense, and we can take the A.
Finally, without me, there is no gear - this one's a stretch, but the letter "u" isn't in gear. TBH can't really make sense of this one
Luau, a word for party. Why does this work? If you look at the line "Ultimately, the riddle's now", it bears a striking resemblance to "the party is now!" If we replace the word "riddle" with luau, it seems more like something we'd hear in modern language; "The luau (party) is now!"