Can an arduino nano use a 16.384MHZ clock without any problems?

I am working on a project that uses a 328p outside of a normal arduino and needs i2c, but i can only find a 16.384mHz THT quartz at LCSC.

The processor can operate up to 20 MHz but all the clock derived timing will be 16384/16000 faster. Hence you could have problems with serial and so on. It is possible to change that in the configuration files for compilation. I have no idea what LCSC is, so I can't comment on whether you could just try it.

Hopefully, you have a prototype to test before you go to PCB.

LCSC is a website where you can buy components. I don't really understand how I2C will react to a faster clock. I'll try first on a breadboard and if it doesn't work I'll just search on other sites. Thanks for your help!

MCUdude's MiniCore has options for 18.432MHz and 20MHz, as well as several slower crystal frequencies, if you don't want to worry about making changes for the crystal frequency yourself.

Is this for your watch project in your other post? Note that the maximum frequency the atmega328p can operate at is dependent on the supply voltage, for battery operation with an RTC to do the actual clock timekeeping, I'd be inclined to run the internal oscillator at a lower frequency and put the processor to sleep when not needed.

I don’t really understand how I2C will react to a faster clock.

I2C is clocked by the interface, it does not have to synchronise with anything else as serial UARTs do. The difference between 16.000 and 16.384 is trivial and will have no effect whatsoever on I2C.