Although the club has not won any mayor trophies, it has produced four Olympic gold medalists: Valter Matošević, Alvaro Načinović, Valner Franković and Mirza Džomba.

Four additional Olympic gold medalists played for the club, including Irfan Smajlagić, Vladimir Šujster, Zlatko Saračević and Božidar Jović, and Jakov Gojun, who has a bronze medal.

The club was founded in September 1957,[1] as RK Partizan Zamet by Prof. Stanko Jerger, Josip Šarić and Vittorio Drog.

This decade saw players such as Marijan Seđak, Williams Černeka, Valter Marković, Željko Milanović, Darko Srdoč, Damir Čavlović, Boris Komucki, Renato Sošić and Jurica Lakić who left their marks in Zamet and handball in general.

In 1981, Zamet beat long time city rivals RK Kvarner and became Rijeka's top handball club.

Unfortunately Zamet lost in the first round to Pivovarna Laško Celje on aggregate due to one goal, winning the first match and losing the second.

Zamet finished 8th with coach Žiljak being replaced mid-season with Darko Dunato, who had retired as a player the previous season.

In this season a new generation of players emerged such as Mirza Džomba, Nikola Blažičko, Renato Sulić, Milan Uzelac, and Igor Saršon.

The 1996–97 season saw Zamet in 5th place, a disappointing result due to the fact that they had players such as Valter Matošević and Irfan Smajlagić.

[5] With Damir Čavlović as head coach Zamet played Europe, each season making some of the best results the club saw.

After a successful period, poor results ensued, and during the late 2000s the club often finished in the middle or bottom half of the table.

[11] Over the summer president Devčić gave out statements that most of the club's debts had been paid, starting the season of on a positive note.

[13] Zamet finished their regular season in third place, qualifying for the Championship play-offs for the first time in ten years.

During the summer of 2016 Zamet lost key players Dario Černeka, Dino Slavić, Luka Kovačević, Petar Jelušić and Bojan Lončarić, beginning their season fairly weaker.

[20] Two days later, on the 19th, Zamet faced Ribola Kaštela at home and entered their first win in the Premier League with a score of 35:28.