Here are my immediate thoughts:
There is a “bow” in line 1, it is “stretched” in line 2, and something “flies” in line 3. So this could be a description of someone shooting an arrow from a bow by stretching the bowstring. However, “filled” in line 1 doesn’t fit very well with this idea: it is not clear what it means to describe a bow as “filled”. So maybe I am on the wrong track with this idea.
In line 3, it is not an arrow that flies from the bow, but a “smile”. So this could be a metaphor in which the archer is happy with how good their shot was, so that they smile with pleasure at hitting the bull’s-eye. This idea is reinforced by “with zest” in line 2, which could mean “enthusiastically”.
In a short poem where there is no “reality” to ground us, a metaphor can work either way. So the poem could be a description of someone’s smile, that is “stretched” by the muscles of the face. Perhaps the smile is metaphorically a bow due to its shape. This makes better sense of “filled” in line 1, because lips can be thus described (“filled” meaning “plump”).
The trouble with this idea is that if the smile is (metaphorically) a bow, then it seems to be shot from itself in line 3. But a bow can’t be its own arrow! So maybe I am on the wrong track here too.
“Flies” can mean “flies away; flees” so maybe it is a description of a fleeting smile. This could work with “stretched” meaning “strained” but not with “zest” which only has positive senses.
So however I arrange things there is a piece that won’t fit.
As an aside, I would be cautious about describing a poem as a “haiku” unless it is written in the Japanese language. The haiku form traditionally has three requirements:
- Seventeen phonetic units (音, on) divided into groups of five, seven, and five.
- A juxtaposition of two ideas or descriptions via a ‘cutting word’ (切れ字, kireji).
- A word relating to a season (季語, kigo).
Since the English language doesn’t have on or kireji or kigo, I think it’s better to describe short poems like this as “inspired by haiku” and not “haiku” tout court.