Opening up your data is part of good research practices. It increases the visibility of your work, leads to higher citation rates (twofold is not uncommon), and being transparent about your research shows integrity and credibility.
The EUR requires you to open up your research as much as possible. Many funders and journals have a similar policy and require you to provide a data availability statement during the grant application or submission process. This not only means that you have to prepare data for sharing, research itself should be designed with sharing in mind.
Opening up research is good practice, but not all research can be opened up. For example, when you are working with proprietary data, or very sensitive data, or if there are any reserved rights on the data you used. If this is the case, the EUR Data Repository allows you to put an embargo on the data. That means that after the data is published, it is visible in the repository but not openly accessible. If access is required, a request has to be made to the owner. If applying an embargo is recommended to you, make sure that you state how access can be required, and under what conditions.
It is understandable you have questions or concerns about opening up your data and whether or not an embargo should be applied. Your faculty data steward can help you address these issues.