In Lord Alfred Tennyson's poem "Ulysses
," it is very clear to whom the titular figure bequeaths the island: his son Telemachus. In the pertinent stanza, Lord Tennyson wrote the following:
This is my son, mine own Telemachus,
To whom I leave the sceptre and the isle,—
Well-loved of me, discerning to fulfil
This labour, by slow prudence to make mild
A rugged people, and thro' soft degrees
Subdue them to the useful and the good.
Most blameless is he, centred in the sphere
Of common duties, decent not to fail
In offices of tenderness, and pay
Meet adoration to my household gods,
When I am gone. He works his work, I mine.
Tennyson was very close to Arthur Hallam, whose death struck the poet hard and which influenced his writing. Hallam's death in 1833 coincided with the publication of Tennyson's volume Poems
to negative reviews, and the poet seems, according to at least one scholar, to have become almost obsessed with the notions of death and legacy. In his essay
"Memorials of the Tennysons" (published in Memory and Memorials: From the French Revolution to World War I
, Routledge, 2000), Mathew Campbell suggested that "Ulysses" was a product of its author's grief over his friend's death, and that Tennyson was writing "an act of abdication" in which the master steps down from his position of power, bequeathing to his son the power and responsibilities that once lay with him. The action of Ulysses/Odysseus in turning over to his son Telemachus "the scepter and the isle" suggest exactly that: the leader, no longer able or willing to go on, handing over the reins to the next generation.
The answer, then, to the question of "who will rule the island when Ulysses retires" is Telemachus, Ulysses's loyal and brave son.