I guess your old PAiA has banana jacks (I've seen people swap them for other types). You could buy something like this, or make one yourself:
https://www.low-gain.com/shop/p/utl1e
(If you have a ground banana jack in your 4700 system (or on its PSU) this should be connected with ground in the eurorack system.)
As I don't know much about PAiA systems, I can't say if the audio signal levels or control voltages will match.
It is usually not a big problem, but you need to know if the PAiA can't handle negative voltages, like bottom halves of LFO signals. This can be solved of course.
Also, eurorack uses the 1 V/octave standard (filters, VCOs).
For a comparison with you 4700, this is the Doepfer signal standard: https://doepfer.de/a100_man/a100t_e.htm#:~:text=Signals%20in%20the%20A%2D100
This standard does not cover all eurorack manufacturers/modules unfortunately. Mainly, there are differences in envelope voltage levels: +5, +8, +10 V. This may not matter too much, but it will decide to what extent you can open a filter or a VCA.