When Love with unconfinèd wings Hovers within my gates, (1-2)
Here Love is personified as having "wings" and enjoying lots of freedom. Love, it seems, is very closely related to one's ability to break "free" from a bad situation.
When I lie tangled in her hair And fetter'd with her eye, (5-6)
Love is sometimes a form of confinement—words like "tangled" and "fetter'd" tells us as much. This doesn't necessarily mean that being in love is like being in prison. It can, however, make us feel as though somebody has control over us.
Our careless heads with roses bound, Our hearts with loyal flames; (11-12)
"Roses," "flames," and "hearts"—those all make us think of love. The speaker and his friends' loyalty to their king isn't just obedience; it is almost like passionate, heartfelt love.
The sweetness, mercy, majesty, And glories of my King; When I shall voice aloud how good He is, how great should be, (19-22)
The litany of adjectives here—"sweetness, mercy, majesty," "glories," "good," "great"—suggests that the speaker's feelings for his king are very strong. While he doesn't call it love, it definitely seems like he feels a lot of affection for his liege. The best evidence? Well, it's this very poem, of course!