The poem is full of alliteration that helps to evoke specific sounds or images, to emphasize the speaker's mournful tone, and to reinforce connections between certain words.
In line 1, for example, the sharp, crisp alliteration of "count the clock" and "tells the time" helps evoke the repeating, regular ticks of a clock, and thus sonically suggests the incessant and unstoppable march of time.
Other moments of alliteration simply add emphasis to certain phrases, as is the case when the speaker says that the "violent" in line 3 is "past prime." The alliteration makes the speaker's assertion that this flower's beauty has faded all the more forceful. The strong alliteration in "Borne on the bier with white and bristly beard" works similarly, with those repeated, heavy /b/ sounds also evoking the steady thump of a funeral march.
More subtly, the poem uses alliteration to strengthen connections between important words in the poem and to suggest transitions from states of youthful beauty to states of aging and decay. For example, line 4 suggests the shift of hair from "sable" (black) to "silver'd." And in line 7, the "green" of summer becomes "girded up" in bundles. The repeated /g/ sound calls attention to the dramatic change that the plants of summer have gone through—how their state has shifted from one of vibrant and flourishing life to one of being manipulated and tied up by human hands.
But arguably the poem's most significant use of this device is "breed" and "brave" in line 14. The /br/ sound shared between these words helps reinforce their logical connection in the poem. By relating these two words, the poem emphasizes that it is the act of "breeding," or having children, that will directly allow the handsome young man to "brave" (challenge) time when he eventually dies.