Can I work in the public sector in another EU country if I am not a national of that country?
YES — with 2 exceptions:
Your right to work in some EU countries might be temporarily restricted if you are a national of Romania, Bulgaria or Croatia.
National authorities can restrict access to public sector jobs that involve exercising public authority and safeguarding the general interests of the state – like certain posts in the diplomatic service, armed forces, police and security forces or tax authorities, for instance. However, they cannot apply blanket restrictions, but must assess each job individually.
I am a civil servant and I would like to apply for a job as a civil servant in another EU country. Will my professional experience be recognised?
YES — Your new country of employment cannot give you less credit for professional experience just because you gained it in another EU country. Comparable experience must be given the same credit when it comes to deciding salaries, grades and other working conditions. The same applies to access to employment in the public service.
I am in principle allowed to apply for a specific position in the Greek public sector, although I am from Cyprus. However, the Greek authorities tell me I need to have been resident in Greece for at least 3 years in order to qualify. Is that legal?
NO — Any rule requiring you to live in your new country before being allowed to work in a particular public service would be illegal, unless justified by the specific needs of the position in question.