In addition to the above - technically you could apply for an EASA IR even if you had never held one, thanks to the CBIR route, which allows an ICAO IR holder with 50 hours pic under IFR to take an EASA IR test with no exams or training. The examiner tests your knowledge on the day.
So to answer your question, you need to apply for a replacement EASA license which should just be a straight swap, then head to an ATO and either do a few flights in a light twin and an IR test. I'm a little rusty but you might even be allowed find a SIM and TRE for your current type and fly an LST. I think that's what you would do to convert an ATPL.