[2] On 2 October 2008, he made his European debut, replacing the injured Tomislav Butina in the opening minutes of the second leg of their UEFA Cup first round fixture against Sparta Prague.

On 16 September 2010, Kelava kept a clean sheet in a 2–0 home win against Villarreal in the club's opening UEFA Europa League group match of the season.

[5] On 25 August 2015, Kelava moved to Udinese's feeder club Granada, mainly as a replacement to Real Sociedad-bound Oier Olazábal.

He won a total of 15 international caps for the Croatian national under-21 football team since making his debut against Chile U20 in a friendly played in Kuala Lumpur on 20 May 2008.

Bilić was succeeded by Igor Štimac, who also called up Kelava as an unused third choice goalkeeper behind Stipe Pletikosa and Danijel Subašić for the 2014 FIFA World Cup qualification.