connect an oscillator to a transformer
Your transformer's primary inductance is 4.6 mH (according to your circuit). At 1 kHz this has an impedance of about 29 ohms. Normal op-amps won't drive this sort of load. Try adding a transistor push-pull stage or a class A amplifier.

If you read the data sheet you will see that the output is pretty much zero when driving anything approaching 10mA out. The data sheet also indicates that a 1 kohm load is probably about where you should be heading.

So you can either make your inductance a lot higher or make your operating frequency a lot higher or add a buffer than can supply the current needed to magnetize the core.