What is the function of the noun clause in this sentence? that you are ready to graduate is very clear to me.

The function of the noun clause that you are ready to graduate is that of the subject of this sentence.
If you are unsure how to solve this, just change the whole noun clause with a pronoun, and it will become much easier: That is very clear to me. What is very clear to me? That.
Or use that question technique with this example: What is very clear to me? That you are ready to graduate.