What is the brand and type of the GPS module and can you give a link to it ?
What is the voltage of your power supply ?
Which ESP32 module do you have ?
I read your post five times, but I still don't understand it. If the GPS itself runs at 1.8V, then you also need to convert the TX and RX signals. Some ESP32 modules have enough 3.3V output current to also power other things.
VCC (3,3 V) from esp32 will work - but the logic from UART needs 1,8V and this is the point where I'm not really now how to do it.
I'm using an ESP32 Dev Module. But to understand the solution I want to keep it general.
The "bi-directional" level shifters with mosfets are used for the I2C bus. They will weaken the RX and TX signals 30 times But those modules are cheap and available. It will work if you don't use a cable.
You would be better with a normal level shifter (not bi-directional), but I don't know a simple module
When a 3.3V SD card is connected to a 5V Arduino board, then a chip is used to buffer and to do the level shifting. Manufacturers of boards use a voltage divider with two resistors to make the voltage level lower and a mosfet or transistor to make the voltage level higher.
The FETs used on the Sparkfun and other "level shifters" may not do so good with 1.8V signals.
Knocking 5V down to 1.8V is, in this context, a simple matter; raising 1.8V to 5V, or 3V3, is another (op-amp / comparator).