Hazel is a member of Salem's group, having chosen to join Salem after Gretchen's death. However he does not get along with his colleagues, being either indifferent or even sometimes antagonistic with Salem's other lieutnants.
Hazel is Gretchen's older brother. Hazel cared deeply for his sister and her death at Beacon Academy is his reason for wanting Ozpin dead. When she was alive, Hazel was against her joining Beacon to become a Huntress. Gretchen's death had a profound impact on her brother, leaving him a broken and vengeful man who is clearly still grieving despite the untold number of years since her passing.
Salem's Inner Circle
Hazel is loyal toward Salem and dutifully follows her orders, however he's also afraid of her and greatly fears her wrath. But after their loss at Haven, he unintentionally incurs Salem's ire when he attempts to take responsibility for the defeat. He risks her anger again when he interrupts her with further news. As he sees Grimm hands rising around his feet, he reports that Ozpin is taking the Relic to Atlas, and quickly vacates when Salem orders him to depart. In "Our Way", as Salem creates an army of winged Beringels, Hazel admits to Mercury Black and Emerald Sustrai that their master is taking matters into her own hands.
His only acknowledgment of Cinder is to speak ill of Cinder being thwarted by Ruby Rose, though in doing so he also acknowledges her as a peer. Although the two work together at Haven, he shows no outward reaction to her defeat. Regardless, when being questioned by Salem, Hazel still attempts to take responsibility for Cinder's failure to no avail.
The two have no significant interactions but Hazel doesn't seem to be getting along with the disgraced doctor as he gave Watts an unimpressed look while Watts was mocking Cinder for not being able to talk after her defeat caused by Ruby's powers.
Hazel and Tyrian appear to have a unfriendly if not outright hostile relationship as the scorpion Faunus sadistically mocked him and Emerald and Mercury for their defeat at Haven Academy to which Hazel reacted with a glare and told Emerald and Mercury to ignore him.
Hazel fights alongside Mercury and Emerald during the Battle of Haven. But after they seemingly lose Cinder and the Relic of Knowledge, the three of them are forced to retreat. Hazel carries an unconscious Emerald after she overtaxes herself from using her Semblance.
When they return to Salem's palace, he tells them to ignore Tyrian and proceed inside. Later, when Salem orders everyone to clear the council chamber, Hazel urges Emerald to comply and leads her outside. In "Our Way", as Mercury and Emerald watch Salem create a new Grimm army, Hazel explains her actions to them through an old saying.
Ozpin informs Oscar in "Kuroyuri" that Hazel is someone from his past and advises Oscar to be wary of him as a result. In "Vault of the Spring Maiden", the reason why he wants Ozpin dead is because he blames him for his younger sister's death. His vendetta against Ozpin being of such magnitude that he feels the need to kill Oz in every incarnation that he can possibly get his hands on, determined to make him suffer over and over again.
When Oscar has trouble getting a train ticket out of a machine at a train depot due to lack of funds, Hazel shows up and bangs on the machine. This causes a train ticket to fall out of the slot. Before moving on, Hazel advises Oscar not to let a such small obstacle obstruct his path.
When they meet again in Haven Academy, Hazel is shocked to learn that Oscar is the new incarnation of Ozpin. Though he attacks him, he says his blood will be on Ozpin's hands, and he hopes Oscar can forgive him for seeking to kill him.
The pair are seen meeting with Sienna Khan in "Dread in the Air", to gain her loyalty to Salem's Faction. However, Adam enacts a coup and overthrows Sienna as High Leader, a plan Hazel knew nothing about. Hazel is upset with Adam keeping secrets from him, along with killing Sienna when he deemed it unnecessary.
The lack of cooperation between them is shown again in "Downfall", when Hazel refuses to help Adam after he and his forces are confronted by the Belladonnas, armed citizens of Menagerie and the Mistral Police.