There is no direct connection from Zakynthos to Parga. However, you can take the bus and ferry to Patras, take the bus to Preveza, then take the bus to Parga. Alternatively, you can take the car ferry to Killini, Greece then take the drive to Parga.
How to get from Zakynthos to Parga
From Zakynthos bus and ferry to Patras, bus to Preveza, then bus to Parga. 7 h 52 min 43€. From Zakynthos car ferry to Killini, Greece then drive to Parga. 4 h 58 min 57€.