Article 13(f) of the Data Protection Act is applicable in case of the processing that is necessary for the purposes of the legitimate interests pursued by the controller or by a third party. It explicitly states that the public authorities shall not process personal data based on this legal basis when they fulfil their tasks.
Journalistic, academic, artistic and literary purposes
Another specifying provision is relevant for the personal data processing without a consent for certain category of controllers, in particular in media industry. The controller may process personal data, if it is necessary for the purposes of informing the public via a mass media and such a processing is based on the subject matter of activity of the controller (for example: it is a media company) (Article 78(2) of the Data Protection Act).
Guidelines of the Slovak supervisory authority
Slovak Data Protection Authority published Guidelines on the Lawfulness of Processing, no. 2/2018, from 22 January 2019 (in Slovak) available here: https://dataprotection.gov.sk/uoou/sk/content/metodicke-usmernenie-c-22018-zakonnost-spracuvania-aktualizovana-verzia-zo-dna-22012019.