In Homer's use of the term, arete refers to a special excellence in battle, the great triumph of a warrior, and this quality appears many times in the Iliad, especially in Achilles, Hector, Diomedes, and Priam.
Achilles is arguably the most famous and grandest warrior in the story (even though he is also temperamental and difficult). Achilles is driven out of his sulkiness and back into battle when Patroclus is killed, and he fights with a ferocity that is really rather scary. He avenges his friend and then some, increasing his renown as a warrior and his arete, although some people may well cringe at his treatment of Paris. Achilles is indeed a powerful warrior who excels at combat, but he is a morally ambiguous character at best.
Hector's arete is clear in his willingness to defend Troy at all costs. Even though he would prefer peace and a quiet family life with his wife and son, he goes out to fight. Duty calls, and Hector answers with bravery and self-sacrifice even to the death. Hector probably has a greater level of arete than Achilles, for his motives are purer, which makes his actions purer as well.
Diomedes is an Achaean hero, the king of Argos, who is also a fierce warrior, thereby earning his share of arete. He takes over for Achilles while the latter is sulking in his tent and kills many Trojan soldiers. He even manages to wound Aeneas and fights with the gods themselves.
Finally, Priam earns arete in the Iliad even though he is not fighting. He bravely goes out to recover Paris's body after Achilles kills the young man and drags his corpse around the city walls for several days. Priam has great courage in the face of Achilles's rage, and this can certainly count as arete.