Two options: First, you can obtain a resident permit like a Golden Visa and hire an employee to be the legal representative of the company. Second, if you make a branch of your foreign company, then you may ask from a Greek embassy a national visa D as manager of this branch. If they approve, we can proceed with this type of resident permit in Greece.
According to the Article 16 of Greek immigration law in force, resident permits for investment activity are granted to non-EU/EEA citizens (investors or executives) in the context of the implementation of an investment project following a positive assessment of the investment by the directorate for foreign capital at the ministry of economy and development. There are no restrictions regarding the sector of activity or the location of the investment project. The requirement that must be met by the investment is to have positive impact on national development and the economy. The legal framework does not set specific limits regarding the total cost of the investment project. However, an investor applying for a resident permit under this program should contribute to the investment with an amount of at least 250,000, available through his own funds. The holders of this resident permit have access to the exercise of investment activity (as a legal representative, president, board member or chief executive officer).