The answer to your question would be that the complete subject of the sentence is "The most famous annual festival in Wales".
The subject of a sentence is the person, place, or thing that is doing or being something. You can find the subject if you first identify the verb. Then, ask the question who/what verbs/verbed? and the answer to that question is the subject of the sentence. In this case, the question would be as follows: What is the Royal National Eisteddfod? The most famous annual festival in Wales.
