You can grind out cash to buy a new ship with a hyperdrive, either by abusing the 100% markup on galactic market items to buy items low from the NPC's coming to the trade stations on the planet, or the space station, and selling them high at the market terminals. You can also craft bypass chips for money, as the items needed to craft them are plentiful, and they sell for far more than the crafting materials are worth.
You can also grind out the hyperdrive recipe by going to all the buildings that contain schematic upgrades (shelters (not droppods), operation centers, manufacturing plants etc). They will eventually teach you this schematic, it's just a question of RNG. You might also get lucky and find an NPC that will teach it to you through conversation.