Eventually, Edel declined to stay at PSG after his contract was broken down and joined an Israeli club Hapoel Tel Aviv on a free transfer. Edel played two good seasons in Israel before he searched further for new challenges.

During 2004-05 Edel was a part of the Armenian national team and has played six matches for his country, as well as several appearances for the youth national team.

ISL

On August 21, 2014, Edel was elected by Atletico de Kolkata during the Inaugural International Draft as their seventh and last pick. He thus became Atletico de Kolkata's last piece of the puzzle and one of the bigger goalkeeping names in the league. 

Because each team only could contain a limited number of foreign players in the lineup, coach Habas opted to play with domestic goalkeeper Subhasish Roy Chowdhury during the opening games of the season. Eventually, Edel was given the chance and the two keepers were evenly on the play time.

Because of his excellent contributions, Edel became the unchallenged first choice a little more than halfway into the season, and was also the goalkeeper who played the playoffs and eventually the final against Kerala Blasters, which Kolkata won. Many agreed that Edel was the best player on the field in the final match. Indian football legend Baichung Bhutia praised Edel after the game stating "He’s really given the trophy to Kolkata."

Apoula Edel was given an award after the game for the best "Moment of the Match", for thwarting Michael Chopra’s shot in the 83rd minute.

POST-ISL

Shortly after ISL's end, it was announced that Edel woukd return to Hapoel Tel Aviv - the club he left to play in the ISL.