The Civil Service Law and Rules provide the conditions under which permanent employees in the competitive class may transfer to a different title, agency or geographic location. You must take the initiative by contacting agencies directly or by looking for vacancies on the Governor's Office of Employee Relations' website at https://statejobs.ny.gov/(External Link)

State agencies have broad discretion in choosing to fill a particular job by transfer. If you wish to be considered for transfer, you should provide a current resume describing your work experience, and/or educational background and the mechanism you believe could facilitate your transfer.

What Is A Transfer?
A transfer is the movement of a permanent competitive class employee from a position in one title to a position in a different title, or from a position in one agency to a position in another agency. Both positions must be within the competitive class. Transfers are voluntary and occur with the consent of the employee after nomination by the appointing agency and the approval of the Department of Civil Service. Approval by the agency from which the employee is transferring is not required in order for the transfer to occur.

The Civil Service Law defines three different kinds of transfers:

Section 70.1 allows transfer without further examination from one title to another when a sufficient degree of similarity exists between the minimum qualifications, tests and/or duties of the specific titles involved. The appropriateness of transfer is decided on a title-by-title basis at the request of personnel offices of state agencies. This section of the law also allows employees to transfer to another agency in the same title.
Section 70.4 allows transfer to a title which is not similar, but where the employee meets the qualifications for the title. Usually the employee must pass an examination open to the public for the title before transfer can be approved.
Section 52.6 allows transfer between administrative titles at the same or similar salary grade. Administrative titles are those involving law, personnel, budgeting, methods and procedures, management, records analysis or administrative research.

https://www.cs.ny.gov/jobseeker/faq/transfer.cfm

In Spain, a 'concurso de traslados' doesn't involve an exam, as the people who wish to transfer have already passed their competitive exams. My daughter passed her exams as a secondary school teacher in 2020, and last month the Catalan government published this year's provisional list of teachers and the schools that have been assigned to them. Since 2020 until now, my daughter has been doing courses and things to achieve 'merits', as the more you have, the better the chance of being sent to the school of your choice.

Unless there's a change, my daughter has been assigned her second choice. The person who's going to where she would have preferred had twice the number of merits as she did.

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Note added at 2 hrs (2023-03-13 19:43:06 GMT)
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In the following reference, they're called transfer competitions.

Transfer competitions
They are governed by Royal Decree 1364/2010, Order EFP/834/2022 and relevant regulations in the different Autonomous Communities. They are called through the educational administrations with two objectives:

assuring their mobility throughout the whole national territory;
filling the vacancies established in public educational institutions.
Single scale of merits included in transfer competitions
training and improvement courses;
seniority;
belonging to some of the bodies of senior teachers;
voluntary evaluation.
Calls for examinations
biannually: State-wide transfer competitions;
during school years when state competitions are not held: the Autonomous Communities may organise procedures for the filling of posts relating to the territorial area within their administration.
Salaries of teachers participating in transfer competitions
These remain unchanged:

the components that are established at State level: basic salary, allowance linked to the level of the post held, general component of the specific allowance, etc.;
those consolidated at their institution of origin: 3-year, 6-year bonuses, etc.
The following may vary:

The allowances paid by the Autonomous Communities.

https://eurydice.eacea.ec.europa.eu/national-education-syste...