[1][2] Stier was born in Buenos Aires, Argentina[3] and lived in the middle-class Flores district (the same of Pope Francis)[4] in a Croatian expatriate family originating from Samobor.

[3] His paternal grandfather Ivan Stier was an Ustaše colonel and assistant to Vjekoslav Luburić who escaped to South America after World War II.

During the Slovenian-Croatian diplomatic freeze, Stier was the main participant in the behind-the scenes diplomacy effort and mediator between Kosor and the Slovenian Prime Minister Borut Pahor.

[5] In the May 2012 HDZ leadership contest, Stier supported Tomislav Karamarko[8] but was later opposed to the disciplinary proceedings against Jadranka Kosor in February 2013, after the party decided to sanction her because of her appearances in the media.

[11] Two months later, in June, Stier stated that "Croatia must strongly take up the issue of the constituency of the Croatian people in Bosnia and Herzegovina not only on paper but also in practice."

[15] In the second election for the European Parliament in Croatia in May 2014, Stier again won a 26,432-vote mandate as a candidate on the list of HDZ's coalition composed of HSS, HSP AS, BUZ, ZDS and HDS.