Though it is Queen Ananasa who decides when a Damhan has reached the proper knowledge and wisdom for an increase in rank, the Ananasi may call to her if they feel they have been overlooked. (It's generally considered appropriate to remind Mother that you've been very good lately, especially if you really have been.)
The Ananasi must remain holed away in his Sylie for two days in preparation - fasting and meditating - for the Appeal. Once the time is right, the character spends two Gnosis to establish a connection to the Mother-Queen and then speaks to Ananasa - who does indeed listen - and recites the list of accomplishments and goals achieved for the further honor and glory of the Mother-Queen. If the character has indeed reached the proper levels of Renown, Queen Ananasa will reward them with the new Gifts and markings that indicate a higher rank. If not, the character may find himself saddled with a new task which will provide no Renown, as punishment for his hubris.