Stadt Zurich subsidises lessons for full-time students under 25 living within its borders.
This subsidy amounts to about 60% of the cost (e.g. CHF 640 per semester for a weekly 30 minute lesson vs CHF 1540 for those not qualifying for the subsidy) but even so it is by no means cheap.
If you qualify for the subsidy, click the pdf under "Schulgeld" (school fees) on the following page Musik Konservatorium Zurich
for alternatives that might be cheaper, (e.g. a fortnightly lesson, group lessons). The last two columns show the discounted and non-discounted rates.
You would need to get to them pretty quickly if you wanted to start immediately in September, as they follow school terms and seem to be winding down for the year. They respond to emails in English. (Use the "Kontaktformular" - contact form).