The AD&D 2e sourcebook Powers and Pantheons has 2-3 pages of lore about Hoar. 3e does not change that lore much, so this source could be useful for you to imagine how Hoar's faithful see the world. The following summary information is based on this sourcebook.
Hoar has two aspects. The first one is invoked by those seeking vengeance. Whenever someone guilty meets an unfortunate fate that is befitting the crime, Hoar is given credit. His more benign aspect is known in the North, where he is seen more as a god of poetic justice. Many bounty hunters and some assassins pay service to Hoar before a hunt.
This dual aspect is also reflected in his interactions with other powers. For example Beshaba is listed as an ally, as he seems to be happy to unleash bad luck on the deserving. Both Tyr and Shar try to influence him; Shar wants to turn him into a blind servant of bitter vengeance, while Tyr hopes to kindle his black humor and convert his dogma more towards poetic justice.
We note that this dogma can put vengeful justice above law. We can imagine a society which prefers laws and punishment to deter future crimes, and not necessarily to comfort the victims. In such a society, Hoar's followers could in principle go beyond laws if they deem a particular kind of punishment is actually more appropriate for a given crime. They will still need to be just, have a sense of fairness so that punishments fit the crime, but each punishment could be different depending on the offender and the way the crime was committed. (For example, let's imagine a murderer. The law might dictate capital punishment, with some "humane" means. A devotee of Hoar might want inflict pain before the punishment if the original crime was violent.)
Quoting from P&P, page 30:
No injustice is too large or too small for revenge to be sought and a fitting punishment meted out. Actions of this type have caused most town watches and Tyrists to brand priests of the Doombringer as vigilantes and raised the stature of the priesthood to that of champion of downtrodden and underdogs in the eyes of the common folk.