The Kingsguard
The seven white knights sworn to shield the king and his blood with their lives — which at Ashford Meadow puts three of them on the wrong side of a trial of seven, oath-bound to fight for a prince in the wrong.
The fuller tale
Aegon the Conqueror founded the order on a simple, brutal trade: seven knights in white, sworn for life to guard the king's body before anything else, forbidden the lands, titles, and families that might one day give them a competing loyalty to protect instead. In principle it produces the finest, most disinterested swords in the realm; in practice, it produces men who cannot refuse an order regardless of who is giving it or why.
That design flaw shows itself plainly at Ashford. Three white cloaks — Ser Roland Crakehall, Ser Donnel of Duskendale, Ser Willem Wylde — find themselves bound by their oaths to fight on Prince Aerion's side of the trial of seven, not because any of them believes his cause just, but because the order they serve was never built to let personal judgment override the crown's blood. Justice, in that trial, has to be fought for by men who never swore to defend it and against men who were never asked whether they agreed with the side they had been assigned.
It is a small, sharp illustration of the order's whole bargain across its history: perfect loyalty is easy to admire in the abstract and considerably harder to admire once you have watched it march good men into the wrong side of a fight they never chose.
The page and the screen
The white cloaks' presence at the trial of seven is dramatized in the aired Hedge Knight season largely as the novella describes it — Kingsguard members obligated to a side rather than a cause — though the order's deeper institutional history gets fuller treatment on the page than the show has yet had reason to give it.