To develop a 3-electrode system on flexible substrate, after the screen printing the gold conductive ink (to act as working electrode) on the PET substrate, how can I make electrical contacts with the clips of potentiostat?
You need to have some "wire" to go to a contact point on the edge, and you need to have an insulating substrate over that wire leaving the contact and the electrode area exposed. There are different means to the end, but you have to account for contact in your manufacture.
You can connect one corner with copper wire then cover that corner and wire with aluminum adhesive foil ( it is cheap) then insulate that corner with epoxy. then check the conductivity before using the electrode.
Use high-quality epoxy and give it the full time of curing to avoid crevice corrosion.
There are small commercial connectors with a hook that you can use, but also those in Anal. Chem. 86 (2014) 11999 or Biosens. Bioelectron. 93 (2017) 40.