There are 3 airports on the the Mediterranean island of Cyprus.
You can enter North Cyprus directly via Ercan International Airport Ercan (ECN), which is near Nicosia and approximately 40km from Kyrenia/Girne.  There is normally a brief stopover in Turkey on the way to Ercan and, there is no need to leave the plane.
 
Ercan International Airport- Nicosia
www.flyercan.com
www.ercanairport.co.uk
Phone: +90 392 600 50 00
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There are two more International airports located in the South.
 
The main one is at Larnaca, which is approximately 85km from Kyrenia/Girne.  It is necessary to go through the border with the North en route.

Hermes International Airport-Larnaca
www.hermesairports.com/en/larnakahome
Phone: +357 777 78 833
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The other entry point is at  Paphos, which is approximately 165km from Kyrenia/Girne.

Paphos International Airport
www.hermesairports.com
Phone: +357 777 78 833
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Flights To North Cyprus:

Turkish Airlines
official website
 
Pegasus Airlines
website for booking and details:

Anadolu Jet

(hyperlink needed)

 
 
Flights To South Cyprus:
 
Easy Jet
www.easyjet.com
 
British Airways
www.britishairways.com
 
Aegean Air
http://en.aegeanair.com
 
Ryan Air
www.ryanair.com

Cyprus Airlines
www.cyprusairlines.com
 
Emirates
www.emirates.com