If there is not a complete conducting circuit then the emf induced in the secondary does not produce andan induced current and this in turn means that there is no induced magnetic field produced by the secondary coil.
If the secondary coil does not produce an induced magnetic field then the primary will not know of the "presence" of the secondary coil and so the primary circuit behaves as though there is no secondary coil present - ie as a self inductor.
. . . thus no current flows through the Primary.
That being the case there will be a current in the primary and if there was no resistance in the primary circuit and it was an ideal self inductor then the current and the applied voltage would be $90^\circ$ out of phase with one another which means that on average no heat/energy is dissipated in the primary circuit.
If that secondary circuit is completed then the induced emf in the secondary induces a current in the secondary which in turn produces an induced magnetic field which the primary coil can "feel".
This induced magnetic field due to the secondary then induces an emf in the primary which then changes the phase relationship between the primary voltage and current.
With a resistive load and an ideal transformer the current and voltage in the primary are in phase with one another.