Yiasou!
The problem you will come up against is the speed (or lack of) response from the Hellenic DCA. Bearing in mind Greek Easter is only a short while away... Research some other threads, others have had issues.
They will need to verify and release your medical records to the CAA or IAA (to which authority are you converting, UK or Ireland?)
All ratings will need to be current to be included in your new licence.
I personally converted my UK professional licence to Irish (IAA) for various reasons, not least that I no longer live in the UK. The Irish are a great bunch of helpful people in FCL. Nothing is too much hassle.
Oh, and your Greek licence is an EASA licence.
From your profile, if the 737 is on your foreign ICAO licence, the IAA (Irish) will include any current foreign type ratings on the IAA licence. They will, however, be restricted to the country of issue.