The Mentor Merit [CofD 51] focuses on relations within mundane or supernatural society. While both of those can be of great help to a Noble, a further option is available to a lucky few: personal mentorship from their Queen. Even though a Queen cannot leave the Dreamlands, she still has such a wealth of power and experience that she would be far beyond a five dot Mentor. However the Queens have many obligations that demand their time besides tutoring a Noble. Therefore when applied to a Queen, the Mentor Merit represents not her skill, but how much of her attention she will bestow upon the character. As a general rule you may assume a Noble gets at least one session with her Queen per week for each dot she has in Mentor (the Queen). A session can be just a few moments before the throne, but at high dots it can be significantly longer.
Even without any dots in Mentor, a Noble is always welcome to attend court, but unless she has important business the Queen will focus her attentions on those who do. When the PCs have an emergency they can usually get a chance to explain and some advice; the amount of time received depends on how serious the emergency is, and whether the Noble should be able to handle it or needs significant help. (Remember that both of these are opinions and two Queens might see the same situation differently. The Queen of Swords considers losing a boyfriend as roughly equivalent to a small crisis. Even her own followers often think that's taking things too far.)
When portraying the Queens the Storyteller should always remember that they have had no contact with Earth for millennia and are consequently out of touch. Therefore no matter how many dots a Noble has in Mentor and no matter how important it is, the Queen of Hearts cannot teach her followers how to navigate the Chinese political system. She simply does not have that knowledge. She can teach the Noble Skills or direct her to appropriate Charms, but it would be up to the Noble to translate that into an appropriate plan of action for the modern day. For similar reasons, a Radiant Queen cannot buy equipment or services on Earth for one of her followers - Resources is not available from a Radiant Queen as a Mentor.
A Noble must follow a Queen before she can place dots in Mentor in a Queen. Neither Storms nor Mirrors will serve as Mentors. A follower of the Last Empress cannot place more than three dots of Mentor into her Queen - the Queen of Tears' kingdom is under siege and conforms to the normal rules of time, she just does not have enough time to spare. On the other hand, the Queen of Tears can give her favored agents modern money or valuable goods.
With one dot a Noble can usually get the occasional snatch of time whenever there is a lull in court proceedings, enough time to talk about recent events or ask questions and get a brief bit of advice.
At three dots the Queen often has your character's name in the royal itinerary for time with her alone, or perhaps group sessions with her Nakama. She has the opportunity to talk at length about her progress in the war of hope and receive private tutoring. She also knows what her queen is like when she has an opportunity to take off her crown, so to speak. Generally speaking a Noble with three dots of Mentor has something special about her that caught her Queen's eye, something the Queen is especially keen to nurture. She may be the only Onceborn in the Court or run the largest Nation among the Queen's followers. Perhaps she was someone the Queen respected in a past life or maybe the Noble works full time as one of the Queen's agents upon Earth and must report in often (This can be especially helpful for beginner players as it both justifies clear goals for the character and advice from the Storyteller).
At five dots your character is spending at least an hour or so with the Queen most nights, and if they don't show up the Queen may even get worried and send one of her other followers to check on the Noble. This level of attention is exceptionally rare and characters who have five dots are either vital to the Queen's agenda or have an exceptionally strong personal connection. Perhaps the Queen believes the Noble might become a Queen herself and has dedicated herself to making sure it happens. The Noble may be the first Ambassador to a concept the Queen cares for greatly. Alternatively the Queen and Noble might have an immense personal bond of friendship, or maybe the character is the Queen's consort (though this is usually only an option for followers of Swords).