No, you will not need a second EU Visa to other Schengen areas If you have been issued a long stay visa or residence permit already by a Schengen state, you may travel to anywhere within the Schengen state, as long as you respect the maximum duration. This length of time is typically known as “short stays” and lasts for 90 days within a 180-day period.
You may still freely travel within the Schengen area with this time frame.
Traveling within the Schengen Zone
Passport or other form of travel authorization
If you want to travel, you must have a valid passport or other travel document on you at all times. Your passport or travel document must have been issued within the last ten years. Your passport or travel document is valid for further three months after leaving the Schengen area.
Traveling with a short-term visa
You can only enter the Schengen area once if you have a valid single entry visa. In every 180-day period, you are allowed to stay in the Schengen area for 90 days. You are free to travel to and remain in any Schengen country during these 90 days. Are you passing via another nation on your way to the Schengen area? Then you must demonstrate that the Netherlands is the intended destination.
Do you have a valid multiple entry visa that allows you to travel on several occasions?
Multiple entries and exits are permitted inside the Schengen area. When you initially enter the Schengen area, you must declare your main destination.
Do you require a visa?
During the visa-free access period, you can stay in the Schengen area for up to 90 days in any 180-day period. During this time, you are also permitted to enter and exit the Schengen area.
A valid residence permit / national visa allows you to travel between the Schengen countries.
You can stay in any Schengen country for up to 90 days in each 180-day period if you have a valid residency visa or Schengen visa.