Suppose a coil is place in a changing magnetic field and the circuit is not closed will the current induce in the coil?

Strictly speaking electromagnetic induction is a process in which changing magnetic field produces electric current. Because electrons have their own magnetic field when an external changing magnetic field is applied to them they move. The movement of those electron produces current. Hence, we can say that the current will produce. But we are not able to measure it or find out about it for instance as soon as we connect it to the galvanometer circuit is closed which is not allowed in question.

So, finally we will conclude that the current will not produce because:

We do not have any evidence about it i.e. we cannot find out about it.

A current will only flow through wire if the circuit is complete.