It seems very much as if we are presented with a character who is consumed by wander-lust, and although he now has the long-sought for stability and peace that he has endured so much to gain, actually Ulysses finds that this tranquility is anathema to him, and he longs to return to his life of adventure, risk and discovery. Note how his reasons are developed in the first few lines of the poem:

It little profits that an idle king,
By this still hearth, among these barren crags,
Matched with an aged wife, I mete and dole
Unequal laws to a savage race,
That hoard, and sleep, and feed, and know not me.

Note the use of adjectives in these lines to express the speaker's feelings of frustration at his inertia. He is an "idle" king, next to a "still" fire, among "barren" crags. He has to work patiently with a "savage" race. We can understand his frustration when we remember the constant movement and adventure that has characterised his life. His determination to carry his adventure on is expressed in the following lines:

I cannot rest from travel; I will drink
Life to the lees.

In these two lines we see the speaker's determination to extract every ounce of excitement and adventure from life. Compared to this spirit of adventure, his existence in Ithaca is sharply contrasted. Simply put, having spent so much of his life travelling on adventures, now Ulysses finds that the stability and monotony of life ruling his kingdom is killing him, and so he plans one more adventure before he dies.

In Tennyson's "Ulysses," why is Ulysses discontent with ruling his country?

Ulysses grows restless, fueling his discontent. His thoughts begin to stray from staying home to enjoy life with his family. His thoughts also steer him from the desire to rule his kingdom.

Ulysses then begins to relive his heroic travels. Even though he is finally home, the call of the open sea and a chance to rekindle his younger days or the zeal he once had for life, is something he can not pass up.

Telemachus proves to be a fit person to leave the kingdom to; this idea furthers his resolve that another voyage is possible.