Gjuci was born in Aversa, Campania, Italy to Albanian parents from Burrel. He grow up as a player at Sassoferrato Genga from where he was signed by Reggina.
He made it his debut for Reggina at the age of 16 and 8 months during a derby match on 5 October 2014 against Cosenza which was won 3–0 by Reggina, becoming the third youngest debutant in the Reggina's history after Vincenzo Camilleri and Giandomenico Mesto. After Roberto Insigne scored his third personal goal and third goal of the match even, the coach Francesco Cozza decided to give Gjuci the great opportunity to make it his professional debut.
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On 6 January 2015 he managed to score his first professional goal against Martina Franca after playing as a starter and scored in the 25th minute also to give his side the 1–0 victory.[4]
On 14 August 2019, he returned to Serie C, signing a one-year contract with Fano.[6] On 3 January 2020, his Fano contract was terminated by mutual consent.[7]
International career
In an interview after his debut in Reggina, Gjuci admitted that he wanted to play for Albania at international level and would welcome an invitation by FSHF.[1]