Following a loan to Universitatea Cluj in the 2011–12 season, Grozav returned to Romania again at Petrolul Ploiești, with which he won a Cupa României trophy.

His performances prompted another transfer abroad to Russian club Terek Grozny in the summer of 2013, spending several seasons there before moving frequently between teams in Romania, Turkey, and Hungary.

Grozav started his career at his hometown club Unirea Alba Iulia, playing his first match in the 2007–08 Liga II season.

In the summer of 2009, after two years in the Romanian Liga II, Grozav wanted to score a move away at Standard Liège as a free agent.

László Bölöni eventually brought Grozav to Belgium in January 2010, signing for Standard Liège for an undisclosed fee, whilst Unirea Alba Iulia retained 15% of the players rights.

[4] On 8 August 2013, he scored the decisive goal against Dutch outfit Vitesse Arnhem in the 95th minute to make sure Petrolul Ploiești progressed to the Europa League last preliminary round for the first time in the club's history.