Bright Star, would I were stedfast as thou art— (line 1)
In the opening line of the poem, the speaker addresses something non-human, and therefore perhaps part of nature: the "Bright Star," which we know from context means the North Star, or Polaris. From this, would it be fair to say that what the speaker wants is harmony with nature?
Not in lone splendor hung aloft the night (line 2)
But, as have seen, the second line of the poem immediately goes against the impulse of the first line. Instead of union with the Bright Star, and hence with part of nature, the poet says that he doesn't want to be like it. Then again, though, the description of the Star here makes it seem sort of isolated from the rest of nature: it is "lone" and is "hung aloft the night" – i.e., at the highest part of the "night" and therefore above the night, and perhaps above all the rest of nature. So, is the speaker saying that the star is part of nature but is also separate from the rest of nature? Hard to say – looks like we'd better keep reading.
Like nature's patient, sleepless Eremite (line 4)
Well, now the speaker tells us that the star is part of nature – at least in the sense that it is "nature's patient, sleepless Eremite." Still, that's a pretty weird description. After all, an "eremite" (an old-fashioned word for a "hermit") is somebody who lives apart from everyone else, in a desolate or barren area. Once again, it looks like the star is part of nature, but is somehow separate from it.