Ulysses, 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 life—not 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 life—his 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 Penelope—has 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 act—to accomplish something.