Why is Ulysses in favor of an adventurous life?

, at the
stage of life in which Tennyson pictures him, is not so much in favor of an adventurous life as
simply any kind of active life rather than the resigned inactivity of his
position in old age.

Tennyson has Ulysses describe conditions in which the
heroic life he had led is now over. He is an "idle king," and his people on Ithaca
have become remote, disconnected from him. The great things have been accomplished, completed,
yet Ulysses doesn't simply want to resign himself to this situation and die:

How dull it is to pause, to make an end,
To rust
unburnished, not to shine in use !

Because he was a man
of action in his prime, Ulysses even in old age doesn't want to give up a real lifenot
necessarily a return to the adventures of the past but just something beyond
one in which he will:

mete and dole
Unequal laws
unto a savage race.

Unfortunately there is also an
inevitable and unsurprising sexism in his attitude. He describes himself as "matched with
an aged wife," apparently forgetting that he is aged as well. Ulysses
is in a state of depression. He recognizes that the glory that was his lifehis youth, the
victory in the Trojan War, his ten years of relentless struggle against every odd in returning
to his homeland, and finally dispatching the suitors who had invaded his house in their efforts
to win the faithful Penelopehas been completed, but he doesn't accept this.

He struggles to find an answer, and says:

'Tis
not too late to seek a newer world...
for my purpose
Holds to sail beyond the
sunset, and the baths
Of all the western stars, until I die.

In other words, he knows death is imminent in some sense, but he
wishes to die still trying to actto accomplish something.