The time you won your town the race We chaired you through the market-place; (1-2)
"Time" is the second word in this poem. In the context of the line, it just lets us know that the speaker is recalling a time in the past. But thematically, by placing the word "time" at the very beginning of the poem, it starts us thinking about the idea of time and changes how we see the other references to time in the poem. How? Shmoop is glad you asked.
The moment in time described in the poem's first two lines is how the speaker, and apparently the whole town, will remember the athlete. Always. It's a dramatic, heroic image—the athlete being carried through his hometown. The contrast of that initial moment of heroic drama and joy with the references to what awaited the athlete had he lived helps make the speaker's point more vivid: if the athlete had lived long enough to face the effects of time, he would not have been remembered in such a glorious light.
Smart lad, to slip betimes away (9)
Elegies usually mourn the loss of the deceased. This one does that, kind of. But in this elegy the speaker also praises the young athlete ("smart lad") for kicking-off sooner rather than later. ("Betimes" means early.) That way, the athlete can avoid the inevitable ravages of passing time. Way to go.
Now you will not swell the rout Of lads that wore their honours out, (17-18)
Here again, the speaker is pitching this whole untimely death thing as a real blessing in disguise. By dying young, the athlete won't have to suffer the inescapable humiliation that awaits most athletes who compete past their primes. By dying young, before time can do its dirty work, the athlete will never see his athletic prowess fade or join the ranks of those that "wore their honours out." Yay team?