From A Power in the World, by Lorenz Gonschor (Perspectives on the Global Past, U. Hawaii Press, 2019), Kindle Loc. 655ff:
The most important aspect of the special relationship with Britain, besides the protection of the kingdom against possible aggression by another Western imperial power (Kauai 2014, 73), was the adoption of what Hawaiian political scientist Keanu Sai has termed a system of “British governance,” a perfect example of similitude, as discussed in the introduction (2008, 39–42). This included equating not only the office of mō‘ī with that of king but also the office of kālaimoku with that of prime minister, including the adoption of the name Billy Pitt (the British prime minister at the time) by Kamehameha’s kālaimoku Kalanimōkū, and the offices of kia‘āina with those of governors, because the British Crown appointed them to head its overseas colonies (Sai 2008, 39). The alliance with Britain also included the British union flag, which was later incorporated in the upper corner of the Hawaiian national flag Kamehameha adopted in 1816 (Williams 1963).
Overall, however, these changes remained rather superficial, and the system of government remained essentially that of a classical Hawaiian state. The core institutions such as the mō‘ī and his executive advisors—including the kia‘āina appointed to govern the conquered islands, the palena of the territorial divisions, and the kānāwai and kapu to regulate society—remained similar if not identical to how they had operated during previous reigns. The one major innovation was the employment of foreigners, preferably Britons, such as the sailors John Young and Isaac Davis, who, as major military and diplomatic aides to Kamehameha, were elevated into the higher ali‘i class. More recently arrived other foreign employees of the king, such as Britons George Beckley and Alexander Adams, the Spaniard Francisco de Paula Marín, and the Frenchman Jean Baptiste Rives were treated much like court retainers of kaukau ali‘i (lower chiefly) rank in the classical system (Kame‘eleihiwa 1992, 59).