In case you are interested in renting out a car or you can do so using a valid international driver's license or national driver's license, provided that this license is valid for the class of vehicle you wish to drive.
Keep in mind that in Cyprus, motorists drive on the left-hand side of the road so if you don't feel comfortable driving there is public transportation around the island such as buses and taxis which you can take to move around the city as well as visit other cities.
Transportation from Larnaca airport can be made either by taxi, which you can get right outside the airport and can cost around €105-€135, or by taking an airport shuttle (for €16) which will take you to a Larnaca bus station and then from there get a bus ticket for €5 to Paphos. (or get the Kapnos Airport Shuttle from Larnaca airport to Paphos)
Taxis from Larnaca airport to Paphos
Paphos airport to ayia napa Transfer | Taxi for Paphos airport to ayia napa (cyprusweb-taxi.com)
Paphos buses
Coach and bus Transport by Osypa buses in Paphos ( Pafos ), Cyprus (pafosbuses.com)
Airport shuttles
Kapnos Airport Shuttle