Gržan went through all the ranks of his hometown club NK Zadar's academy, debuting for the first team shortly after his 17th birthday, on 14 May 2011, coming in the 82nd minute of the home 0-0 draw against GNK Dinamo Zagreb for Luka Begonja.
He scored his only goal for Zadar in March 2013, the game winner against NK Lokomotiva, to Begonja's assist.
[7] He made his first appearance for GOŠK on 23 February 2019, in a 1–0 away loss against FK Mladost Doboj Kakanj.
[8] He scored his first goal for GOŠK on 24 April 2019, in a 1–2 home loss against FK Radnik Bijeljina.
[9] In May 2019, after the end of the season and after the relegation of GOŠK to the First League of FBiH, Gržan decided to leave the club.