Are you trying to scare the birds with the electrical zap or kill them? Either way, 220VDC may not be sufficient. The foot of birds have dry tough scales and little blood flow. Also, you have to be concerned with what happens when a bird, dead or alive is stuck across the plates.
Do you want to turn the transistor on and off to limit the output voltage or to extend battery life?
Do you need the secondary to be isolated from the primary? If they can share a common ground connection then feeding back a control voltage to turn off the transistor is lots easier.
If you must remain isolated, then probably and opto-isolator is the best bet. Use a resistor voltage divider across the high voltage output. The divide tap then is connected to a zener in series with the LED portion of the opto. When the voltage divider reaches the zener turn-on value, the LED turns on in the optocoupler and the output section of the opto then shorts out the BE junction of the transistor. The circuit will stay off until the voltage divider bleeds down the capacitors, then it would automatically refresh itself.
What happens at night? Do you turn it off? While many people are resisting the trend, this sort of control project is really best done in a microcontroller. They are cheap, take few external parts, and can be tailored for many different scenarios. Sure, you have to write the code, but that too is not the task it was several years ago.