It's pretty much one straight road all the way to Elounda, if you've got a Sat Nav it will tell you the best way, if not, you might find google maps helpful.
https://www.google.com/maps/dir/Heraklion+port,+λεωφοροσ+713+07,+Leof.+Nearchou+78,+Iraklio+713+07,+Greece/Eloúnda,+Greecefirstname.lastname@example.org,25.6291512,13z/data=!4m19!4m18!1m10!1m1!1s0x149a5bcf1afc4fa7:0xa9b1c1d0c38fc1a4!2m2!1d25.1509479!2d35.3434372!3m4!1m2!1d25.6617419!2d35.2569816!3s0x149a787fdb7dd00d:0xcae962a10a0aa4be!1m5!1m1!1s0x1490833b5f8b5ad7:0x500bd2ce2ba8940!2m2!1d25.7234164!2d35.2613505!3e0Edited: 8:47 am, May 27, 2019
I don't know why that hasn't shown up as a link, but copy and paste it and it'll give you a route.
If you want directions from the airport then happy to give you these, I am not sure why it’s coming up restricted access ( assuming you are referring to the road up to your accommodation ? ) It is quite steep as we have driven up here to the Imperia taverna, anyway if you haven’t got a sat nav happy to help :-)
The OP said the port, that might be why? I was confused too.
Thanks Ginesy21 didn’t see that :-) yes good point what would perhaps make more sense with the restricted access