One possibility that has often been discussed is that Tyene will try to convince the Faith Militant to accept her as one of the judges for the trial of Margaery Tyrell, perhaps as a false maiden. The case against Margaery is weak and based heavily on fabricated confessions extracted through coercion and torture. However, there is a possibility that a sufficient number of judges who do not care about the truth will be appointed to enable a convinction. Tyene and others may simply view the trial as a tool to damage the enemy alliance and decide to support a guilty verdict in advance. More than almost anything other single action, getting the High Septon to act against Margaery would inflict maximum damage and confusion amongst the Tyrell/Lannister leadership.
Other actions Tyene Sand may take: Convince the High Septon that Aegon was delivered to Westeros as a true king and shining champion to "cleanse Westeros of evil." The HS appears to realize that the incest pertaining to Cersei is true, but he has been lacking an acceptable alternative to the present arrangement in regards to the throne. His answer could lie with Aegon. Perhaps Tyene will urge the High Septon to offer the help of both military orders to Aegon if, as king, he agrees to assist the Faith Militant against its enemies. Most of its enemies happen to be Aegon's as well. The biggest problem for Aegon is that this would cause him problems in areas where R'hllor is believed in as well as create antagonism with the North and Iron Isles. The HS's approval would help a lot against the Tyrells, though, should they continue to support the Margaery/Tommen combination.
If the Sand Snakes discover the truth about UnGregor they will definitely want the High Septon to hear of that. The HS would rise up against the Lannisters upon learning that Cersei/Qyburn are using a corpse animated by dark magic. Qyburn's Area 51 will be something that the Faith Militant will view as particularly loathsome. Resorting to necromancing would probably be a worse offense in his view that simply following another religion.
Will be very interesting to see what Varys thinks of this High Septon as well. Varys may also continue his assassination campaigns.
Whether Jaqen could have assassinated a High Septon, due to the renounciation of the use of personal names by holders of that office, would also have been interesting to know.
Edited by The Sunset King, 08 August 2013 - 06:34 PM.