Ulysses, as portrayed in the poem of the same name by Alfred, Lord Tennyson, is an aging king, a man who has accomplished everything in his life that can be accomplished. He has seen kingdoms rise and fall, has created and taken life, and has become a legendary figure in the myths of his people. After all of his adventures, he has returned home to become the beloved king of his people, and yet even in his old age he feels the stirrings of travel and adventure. He cannot rest, he cannot sleep, because he needs to continue his life, not retire to a slow death as a ruler. His life now will consume him in ways he never intended, and he wants to change his life, to move beyond the accepted virtues of age and become an individual again through his own efforts:

We are not now that strength which in old days
Moved earth and heaven, that which we are, we are--
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.
(Alfred, Lord Tennyson, Ulysses, eecs.harvard.edu)

This yearning for new experiences and new trials is important to Ulysses, since he has defined his entire life around that exact philosophy. To finish his life in quiet contemplation is alien and discomforting; he cannot abide the silence of royal court when compared with the thrills of war and exploration. In defiance of time, Ulysses will venture forth beyond the usual limits of his age and if he dies on this new journey, it is in the pursuit of his own goals, not those of society. Ulysses will not conform or lie down to die, but will seek his destiny, whatever it may be, on his own terms and from his own personal abilities.

How does Tennyson portray death and old age in "Ulysses"?

To me, one of the major themes of this poem is that the speaker (Ulysses) wants to keep experiencing and learning new things.  He thinks that a life spent in one place, doing the same thing over and over again, would be terrible.

This is, to me, somewhat of a commentary on old age (or at least the way some old people live).  He is saying that old age is terrible if you just let yourself become fixed in your ways and thoughts.  Instead, you would need to keep trying to learn about new things.

Death is portrayed in the same way.  He talks about how it "closes all."  If death does this, it would be a very bad thing for the speaker of the poem, who never wants life to be closed, who always wants to experience new things.