Auden honors two traditions here: Yeats and the ode/elegy, and he tries to move the latter toward something new, expanded. At traditional English ode is "typically a lyrical verse written in praise of, or dedicated to someone or something which captures the poet's interest or serves as an inspiration for the ode."
Auden says that Yeats' art lives on, as if it is an autonomous, living thing now detached from its host.
According to my Norton anthology:
Poems about death tend to be concerned not just with loss, but also with what remains after a man or a woman dies. Elizabethan sonnets, like those of Spenser or Shakespeare, often take this idea of something persisting after death and use it in the context of an imagined dialogue between lovers, rather than in relation to an actual death: the lover promises his beloved that even though she must die, she will live on forever in his verses. In the elegy, that living-on after death may be thought of in religious terms, or perhaps in terms of cherished memory, or it may make itself felt by changing those who remain, transforming despair into the resolve to go on with life. This last possibility is what Tennyson's poem, "Ulysses," is all about.
Auden's poem draws on all these traditions as it focuses just on that moment when the words of a poet must begin to live on after his death. The poem which Auden writes is the first step in preserving Yeats the poet. But most important, Auden understands this process of poetic after-life as taking place entirely within history.