There are actually two Sir Hectors in Le Mort d'Arthur. The first Sir Hector we'll look at is Sir Hector de Maris, who it's fair to say has a pretty fraught relationship with King Arthur. Though nominally loyal to his king, his greatest loyalty is to his younger half-brother, Lancelot. When Lancelot is expelled in disgrace from the Round Table after his affair with Guinevere is exposed, Hector stands by him and joins him in exile. By choosing to leave court with his half-brother, Hector is displaying his outright opposition to King Arthur. His hostility towards Arthur is further shown by his willingness to participate with Lancelot in the rescue of Guinevere from execution.
The other Sir Hector is King Arthur's adoptive father. As a baby, Arthur was entrusted to Sir Hector by Merlin the magician, and Hector brought up the boy as his own. Foster father and son enjoy a close relationship, even after the disclosure of Arthur's true parentage upon the death of his birth father, Uther Pendragon. One gets the impression that Sir Hector cares deeply for his adopted son and knows just how special he is. We can see this when Sir Kay, Hector's biological son, claims credit for Arthur's pulling the sword from the stone. Sir Hector intervenes and makes Sir Kay swear on the Bible how he really came by the sword.