There is some dispute about the answer to this question. Some scholars argue that, in the first part of Tennyson's "Ulysses," the king is speaking to himself, while in the second part he is addressing an audience, such as his men. Others might assert that the king of Ithaca is addressing some kind of audience throughout the poem. While it's difficult to say for sure which stance is completely correct, I think that the second argument, that Ulysses is consistently addressing the same audience throughout, is the most correct.

The poem is written in the form of a dramatic monologue, meaning that it is written as though it was meant to be performed during a play written in verse. Thus, it would accordingly make sense that Ulysses is addressing an audience throughout, as the dialogue was meant to be recited in front of others. Indeed, it seems as if the poem is meant to be addressed to the same audience throughout because its three parts effectively lay out the logical sequence of events for Ulysses' plan: he describes his lack of satisfaction, his efforts to see that his kingdom is taken care of, and, in the final section, prepares to set off on an adventure. This sequence of events makes more sense if it's directed toward the same audience, as it provides a clear and thorough explanation for Ulysses' reasons for leaving. Thus, while there's no way to know for sure, it's possible to assume that Ulysses is supposed to be addressing the same audience throughout the poem.