A guy who's getting tired of doing what he always does: that's the best way to describe this guy. This is partly because he's begun to worry just a little bit about getting older, about death. The parts about the sword outwearing its sheath, and the soul wearing out the breast, point to the fact that death is "roving" all over his mind. While he doesn't specifically say so, it sounds like the speaker wants to stop roving—stop messing around—because he's getting closer to death and wants something more out of life. Or rather, he wants to spend the time remaining doing more fulfilling things, getting ready for death, that sort of thing.
Okay, so our speaker is a former rover or wanderer—an ex-partier we might say— metaphorically sobering up and starting to worry about death. Funny, this reminds us a lot of the dude who actually wrote the poem: George Gordon, Lord Byron.
Well that's because this is a really autobiographical poem. Byron included it in a letter he wrote that mentioned many of the same feelings described or implied in the poem: a sense of dissatisfaction with the high life in Venice (where he was living) and an awareness of the fact that he was getting older and wasn't going to live forever. While we should always be careful to distinguish between the speaker and the author, in this case, it's okay to blur the line just a little bit.
So, knowing how personal this poem was for Byron, and how autobiographical it really is, an even better way to think about the speaker is to think of him as a young guy, if not necessarily the young Lord Byron. He can still be considered young (about 29), but he's just on the cusp of not-young. Young-ish? That's better. He's a youngish dude who's starting to feel old. He used to love to go out and get crazy—to rove—but he's starting to get tired of it. After a while, you have to grow up. Sure, the moon is still inviting and bright, and the night is a darn good time for loving, but his heart's just not in it anymore.