The modal auxiliary in the sentence is could. {Function of "could":}
"Could" is a modal auxiliary verb used to express possibility, ability in the past, or a polite suggestion. In this case, it is used to express a polite suggestion or possibility. The modal auxiliary is "could," and its function is to express a polite suggestion.
Final Answer:
The modal auxiliary is could, and its function is to express a polite suggestion.
Fill in the blank with the proper form of the verb as per the subject:
The hermit to the king.