Appa is a Guardian of the Universe and shares similar notes to Ganthet. But he is very different in outlook. Appa believes in a stern and stoic philosophy. He thinks the Guardian's should stand as symbols of eternal power and discipline for the Green Lanterns (and indeed all life) to strive for. He's very short tempered and a bit snide in his comments in this story. He serves as a contentious voice on the Guardian council, often believing that dealing with the day to day matters of Corps members is beneath them. So when Rot Lop Fan shows up he doesn't want to waste the time on a single Lantern and would rather move on to more important things. Creating tension between himself and Ganthet.
Appa is not as big a part, but is included here because of how he relates to Ganthet and Sayd (she's next). He should sound old and wise but in a cynical way. Kind of a cranky old man who pretends to be polite but is very passive aggressive.