well all EZS operation is on the A319 as you well know so you will need to do the Full Type Conversion.
not sure about the question though, are you 737 rated?
at the moment getting a work permit for EZS work if you are 737 rated is impossible. only airbus rated guys/girls are accepted.
don't ask me why, it's easyJet stopping it somewhere somehow.
i do know that if you have to undergo complete conversion to type or join easyJet you will be bonded either via TRSS scheme or DE bonding