[2] He finished 8th in the 2002 Under-12 European Youth Chess Championship, tying with Magnus Carlsen on 6 points while Ian Nepomniachtchi won with 8.

[3] The following year he earned the grandmaster title and won the 2008 Under-18 World Youth Chess Championship, scoring 8 points in 11 games for a performance rating of 2623.

[8] In 2011 he tied for 2nd–7th with Julio Granda, Aleksander Delchev, Maxim Turov, Pablo Almagro Llamas and Mihail Marin at the 31st Villa de Benasque Open.

[11] One of his most notable results to date was a victory over Magnus Carlsen at the 2014 Chess Olympiad,[12] where Šarić finished with a 7/11 score.

He graduated in 2013 with a bachelor's degree in Computer Science from the University of Split, and he lives in Omiš, Croatia, with his wife and daughter.