I just got finished reading the "Ringworld" series by Larry Niven (Ringworld, The Ringworld Engineers, The Ringworld Throne, Ringworld's Children). Should I now read the "Fleet of Worlds" series (Fleet of Worlds, Juggler of Worlds, Destroyer of Worlds, Betrayer of Worlds) and then read "Fate of Worlds" as I've heard that it's a conclusion to both the Ringworld series and the Fleet of Worlds series. I'm new to the Known universe as you can tell.
Read the novel Protector first, if you haven't read it already. It contains backstory that is quite pertinent to the Ringworld books. Also, the story in Protector is directly continued and resolved in the Destroyer/Betrayer/Fate of Worlds trio of books.
Read the Niven short stories "Borderland of Sol", "Neutron Star", "At the Core", and "Procrustes" before tackling Fleet of Worlds and Juggler of Worlds as those novels are partial retellings of the short stories and surrounding events, but from different points of view.
Note that the ... of Worlds books are neck deep in Puppeteer culture and politics. If your interest is primarily about the Pak, stay away except for Destroyer of Worlds, in which the Pak drive the plot from beginning to end.