You chose to translate quite a difficult text and you nailed it! There are just a couple of things I'd suggest you change:
● "It's love"-> "(And) Love". Remember: è= (it) is; e= and. I think you mixed them up. You can either leave the title as "Love" (here "e" doesn't really have much of a meaning, it's there just to give a more poetic atmosphere) or translate it literally as "And Love";
● "in him she had no need". So you're personifying Time as a man, but here I think the meaning is much more literal. She (i.e. Love) didn't need any more time;
● "in the corner of his heart"-> "in the corner of her heart". If it's not specified whose heart it is, then it's definitely Love's;
● "He went away"-> "She went away". I think you misunderstood the text to be about Love and Time, so you've described them as some kind of lovers. As I said, "time" in the first verse had a very literal meaning, so here it's still talking about Love;
● "And he has returned without having left"-> "And she returned without having left". Here the text is explicitly using the masculine form. You chose to personify Love as a female, but "Amore" in Italian is masculine, so "essere partito" still refers to Love. The biggest problem, though, is how you translated the passato remoto. In English a simple past was enough, no reason to resort to a present perfect. You correctly used the simple past in the previous line, so I'm not sure what happened here.