There are several countries that directly issue work permits after student visas, provided that it is under the domain of certain terms and conditions. The top in the list to offer the amazing opportunity is New Zealand followed by Canada, Australia, the U.K., the U.S.,

The visa allows a stay of a year elongated to a couple of them and even 3-5 years depending on the guidelines of the specific country in terms of qualifications, occupational capabilities, registration, etc. 

• New Zealand- 1, 2, or 3 years.
• Canada- Up to 3 years.
• Australia- 1.5 years, 2-4 years, or 5 years for various domains.
• The U.K.- Up to 2 years and extension to 3 years upon several terms.
• U.S.- 6 months, 1 year, 2 years, or 3 years dependently.

The work permit is extendable in some countries under numerous terms and conditions. While some countries may prohibit doing the same. It is therefore crucial to know every piece of information related to this on a strict prior basis.