In a closed circuit, electric current is induced so as to oppose the changing magnetic flux as per conservation of energy. However, in open circuit, emf is induced across its ends. How it is related to flux change?
If you have a complete conducting circuit then an induced emf will produce an induced current in the circuit.
The direction of the induced current will be such as to oppose the change/motion producing it which is Lenz's law.
If there is no induced current then there will be no opposition to the motion.