Gabrić made his 1. HNL debut on 16 September 2006 in a home match against Varaždin, replacing double goalscorer Josip Balatinac in the 80th minute. Varaždin again proved to be a favoured opponent for Gabrić, with his first Hajduk goal coming against the same side on 17 March 2007. He scored two further goals by the end of that season, one against Međimurje and the other against Zagreb. When Robert Jarni was appointed as head manager of Hajduk, Gabrić became a more prominent member of the first team, managing 23 appearance in the 2007–08 season. His side struggled, though, as they finished in fifth place in the league, 30 points behind league champions and fierce rivals Dinamo Zagreb. Under Jarni, Gabrić played in a variety of positions al across the midfield and even occasionally in defence. After Jarni resigned, Gabrić blossomed under the management of both Goran Vučević and Ante Miše, with both managers using Gabrić in a more advanced role either as a right or left winger or even as a number 10 behind the striker. This improved his scoring return, with the player netting eight times in 30 league games in the 2008–09 season. In December 2008, Gabrić signed a new three and a half year deal with the club worth a rumoured amount of €180,000 annually. He also receive the Heart of Hajduk Award as a result of his performances in the 2007–08 season.
In August 2009, Gabrić was signed by Turkish giants Trabzonspor in a €2.5m deal. He made 28 appearances in his maiden year in Turkey, scoring four times but largely struggled to impress and was therefore sent out on loan to MKE Ankaragücü for the 2010–11 season. At Ankaragücü, Gabrić made 26 appearances and again scored four league goals. On 23 June 2011, Gabrić was seriously injured in an accident after losing control of his car on the A1 motorway near Split, Croatia. He sustained a fractured skull and was in a coma for four days. His club at the time, Trabzonspor, terminated his contract. After the accident, Gabrić was initially unable to walk, and had to undergo extensive rehabilitation in order to regain his motor skills. He filed a suit against Trabzonspor for breach of contract, which ended in settlement in 2014.
Return to Hajduk Split
In September 2011 Gabrić signed for Hajduk Split. He made his return to football on 5November 2011, in a round 14 1. HNL clash against NK Varaždin, the side he made his debut against and scored his first professional league goal against. He made another nine appearances that season but largely disappointed.
Rijeka
In June 2012, Gabrić moved from Hajduk to Rijeka on a free transfer, following his father's footsteps, who made the same move. At Rijeka, Drago again struggled to impress and was dropped from the squad for the last 14 matches of the season. He moved on loan to Slovenian side NK Domžale for the 2013–14 season, but once again having a poor season, scoring once in 14 games and hardly playing a part in the side's second half of the season. Upon his return to Rijeka and with one year still left on his contract, Rijeka manager Matjaž Kek dropped the player from the squad completely and so Drago was forced to play with teammate in a similar situation Mehmed Alispahić in Rijeka's second team - playing in Croatia's third division. Later on, Gabrić continued his career in Zadar where he played under the tutelage of former Croatia national football team manager Igor Štimac.
