There are many companies that rent cars and motor bikes in Karpathos island and all of them are based in the capital (Pigadia, Karpathos).
Hermes Rent A Car (Mrs. Despina Dargaki) :
email : ermis_cars@yahoo.com
tel1. +30.22450.23979
tel2. +30.6974873117
http://www.facebook.com/pages/Hermes-Rent-A-Car/185615814809957?ref=ts
Billy’s Rent a Car ( Mrs. Christina Karaksi) :
URL : www.billysrentacar.com
Tel1. +30.22450.22921
Tel2. +30.6977.887875
You can find petrol stations only in the capital of the island (Pigadia), as well as on your way from the airport to Pigadia. So be very careful to have a full petrol tank when leaving the capital for driving to the rest of the island.