Yes. Article 23 of the General Data Protection Regulation (GDPR) and various provisions under the Data Protection Act 2018 (such as section 60) set out a number of circumstances in which your right to obtain a copy of your personal data can be lawfully restricted  by a data controller. This is necessary in order to strike a balance between the rights of the individual, on the one hand, and some important needs of civil society, on the other hand. However, if the right to access your personal data is being lawfully restricted or curtailed by a data controller, the data controller must specify why and state what legislative provisions they are relying upon.

For example, a criminal suspect does not have a right to see the information held about him by An Garda Síochána where that would impede a criminal investigation. Similarly, you do not have a right to see communications between a lawyer and his or her client, where that communication is subject to legal privilege (section 162 of the Data Protection Act 2018 provide for legal privilege). The right of access to medical data and social workers' data is also restricted in some very limited circumstances, where the health and mental well-being of the individual might be affected by obtaining access to the data.