Connecting PLC output to an Arduino

Are there anyways of connecting PLC output to an Arduino?
Like different output from PLC runs different functions in the Arduino.

Yes. Watch the voltage levels and select a proper interfacing circuitry.

Is using PLC output to activate relay which then complete the Arduino power suitable?

Yes, that would work. Better woukd be to use an opto coupler as it's lifetime is much longer.

Appreciate the advice, thanks!

Is the relay in a PLC I/O module or is it external?