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In Larry Niven's Known Space novel Protector, Phssthpok, a protector-stage Pak, traveled thirty-one thousand light years across the galaxy to rescue a failed Pak colony on Earth. Phssthpok used a Bussard ramjet for propulsion, travelling for centuries at sublight speeds to make the journey. Through other Known Space stories we know that the Pak were responsible for most if not all the Slavers' high technology, such as the hyperdrive, the stasis field and the disintegrator. We also know that they were one of the few intelligent species that survived Suicide Night.

Given this, why was Phssthpok not using hyperdrive? Why were the later Pak refugees from the core explosion also not using hyperdrive? Niven's novels are information dense so it is certainly possible that I missed or forgot the explanation.

Because the Pak didn't have it. Their technology was not that advanced, really, at least in Pssthpok's era. (If they built the Ringworld, some must have been more advanced, at one point.)

At the time Pssthpok showed up in Sol System, humans had invented the ramscoop, but didn't have manned ones yet; on the other hand, Brennan considered Pssthpok's ship pretty poor:

It's not that good a design, I could improve it blindfold, but you could buy Ceres with the monopoles!

And figuring out the tree-of-life/thallium issue was a serious difficulty for the united childless protectors of Pak under Pssthpok:

Oh, that's no mystery. Though it had the protectors of Pak going crazy for awhile. No wonder a small colony couldn't solve it.

Given the extreme intelligence of protectors, that implies their knowledge of biochemistry must have been (at the start of the project) below ours now.

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The "surviving Suicide Night" thing, if correct, must have been established in much later material & wasn't part of the original idea. (Given that the Pak are very biologically similar to Earth life, they must be descended from Thrintun food yeast - like the Kzin, who can eat humans - and thus be much later than the Slaver era.)

Even if it's now canon (and IIRC the Man-Kzin Wars stuff generally isn't), the Pak tend to lose technology:

I told you, they can't keep their technology. Whatever can't be used immediately, gets lost until someone files it in the Library. Military knowledge never gets filed; the families keep it a deep, dark secret. And the only ones to use the Library are childless protectors. There aren't many of them, and they aren't highly motivated.

Also, the Thrint FTL drive wasn't the Outsider hyperdrive, it was some kind of jump drive that worked on a different principle... possibly shifting directly into a very high layer of hyperspace that makes the jumps effectively instantaneous. It's also apparently unreliable, where you come out is uncertain, and it seems to have some kind of psionic equivalent of the Blind Spot. Here's how World of Ptaavs opens:

There was a moment so short that it had never been successfully measured, yet always far too long. For that moment it seemed that every mind in the universe, every mind that had ever been or that would ever be, was screaming its deepest emotions at him.

Then it was over. The stars had changed again.

Even for Kzanol, who was a good astrogator, there was no point in trying to guess where the ship was now. At 0.93 lights, the speed at which the average mass of the universe becomes great enough to permit entry into hyperspace, the stars become unrecognizable. Ahead they flared painful blue-white. Behind they were dull red, like a scattered coal fire. To the sides they were compressed and flattened into tiny lenses. So Kzanol sucked a gnal until the ship's brain board made a thudding sound, then went to look.

Because the Pak never had hyperdrive.

The Slavers' clever slaves were the Tnuctipun, who all died. No-one except the Bandersnatchii survived Suicide Night.

The Pak evolved later and never discovered the hyperdrive.

Pak with hyperdrive would have resulted in a burnt-out galaxy within a few years!

You're thinking of the revelations from Man Kzin Wars XI, "Teacher's Pet", in which it's revealed that the Pak were engineered by the Tnuctipun.

Fortunately, that seems to be non-canon, since nothing really holds together at all if that's true.. any Protector that saw Hyperspace or even knew it existed would presumably figure out how to build a Hyperspace drive in short order.

The U.N. bought the hyperdrive from the Outsiders - interstellar traders of impeccable ethics - and used it in the Man-Kzin wars.

The Outsiders didn't use the hyperdrive themselves, preferring to remain in Einsteinian space, for reasons of their own. When Louis Wu asked an Outsider why this was so, the Outsider answered, "That information will cost you...."

The Pak would have done everything in their power to completely wipe out the Outsiders, had they come into contact with them. The Pak detest any intelligent life form other than the Pak.