On monday mornings, the anxious birds watch rather closely for the increasingly rare visits by the rest of the flock. which underlined adverb describes another adverb?

There are only two adverbs next to each other in the sentence, and those are the words rather and closely. So, the correct answer is rather - that is the adverb that describes another adverb - closely. You can ask the question - How closely?, and you will get the answer - Rather (closely), which describes the adverb closely.
There is another adverb in the sentence - the word increasingly, but it is describing an adjective rare, and not an adverb, which is why it is incorrect.

Ahhh yes i love the divine comedy gimme a bit and i’ll have a bunch of stuff for u