Estonia has working holiday agreements with Australia, Canada, New Zealand. Granting the right to work to 18–30 year olds who may stay in the Republic of Estonia for up to 1 year.
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New Zealanders between the ages of 18-35 years are eligible to apply for 43 long stay visas under the working holiday schemes New Zealand has agreed with other countries.
40workingholidays.com has guides on how to apply for the visas, and how to get setup once you arrive.