Short answers, pulled from the story.
Albert Henry became the first prime minister of the Cook Islands on the 4th of August 1965, the year the islands gained self-government. He served until the 25th of July 1978 and won four elections, in 1965, 1968-1972 and 1974.
The title of Premier for the Cook Islands' head of government was replaced with Prime Minister in 1981. The change took place during Thomas Davis's first term in office.
Mark Brown is the current prime minister of the Cook Islands. He took office on the 1st of October 2020 and was elected in his own right in 2022.
Henry Puna served as prime minister of the Cook Islands from the 30th of November 2010 to the 1st of October 2020. He was elected in 2010 and re-elected in 2014 and 2018.
Thomas Davis and Geoffrey Henry both served more than one separate term as prime minister of the Cook Islands. Davis held office in 1978-1983 and again in 1983-1987, while Henry served briefly in 1983 and again in 1989-1999.
The Cook Islands Party has held the office more than any other party, through Albert Henry, Geoffrey Henry, Joe Williams, Henry Puna and Mark Brown. The Democratic Party, the Democratic Alliance Party and the Cook Islands First Party have also held it at various points.