Tennyson uses two elements in his poetry that could be described as romantic.
First, romance literature goes back further than the romantic poets such as Wordsworth, Shelley, Coleridge, etc. It goes back to the Middle Ages or medieval period. Tennyson uses characters going back to romance literature from that period. In "The Lady of Shalott," he writes of Camelot and Sir Lancelot. These are characters from the romance tales of the Middle Ages. He hearkens back to the past.
Second, he uses classical allusions, and writes of classical characters. In "Ulysses," he imagines Ulysses twenty years after Homer's Odyssey ends, bored and cranky and tired of being a stationary ruler. Ulysses wants to get back to the sea and seek more adventure.
Of course, Tennyson puts his Victorian spin on these romantic subjects. Both the Lady of Shalott and Ulysses are thinly disguised artists. Both characters and their poems deal with the relationship between artists and their art and their reality.