Two months after Elseid's birth, his father Gëzim emigrated to Italy, like many Albanians had done in the 1990s, in search of employment opportunities in order to provide for his family.

Hysaj himself started his youth career aged 7[4] with KF Shkodra, an amateur club based in his birthplace Shkodër and managed by Taip Piraniqi.

When Elseid had turned 14 he traveled to Italy where he was assessed by Piccioli and attended trials at various clubs, including Fiorentina before eventually joining the Empoli academy.

The goal came in the 4th minute after he received a pass in the entrance area, made an zig-zag move between three opponents then issued a left-foot shoot, which was stopped at the gate of the squad triangle, but the strike was not enough, as Empoli loss the match within 2–1 result.

[22] Hysaj begun in the best way possible the year 2015, because after a goalless draw with his squad against Verona, he was selected by sports analysts in the best lineup of the 17th week of Serie A.

[24] In July 2015, Hysaj concluded a deal with the fellow Serie A side Napoli, following former Empoli coach Maurizio Sarri and player Mirko Valdifiori to the club.

[28] He showed an impressive form at the club to become a regular starter under the coach Maurizio Sarri and also playing the entire 90-minute matches, substituting off in just a few cases and leaving behind the Italian international Christian Maggio.

[29][30] Hysaj made his European debut on 17 September 2015 in the Europa League group stage match against Club Brugge, which ended in a 5–0 home win.

[37] Hysaj made his 100th appearance in all competitions for Napoli on 21 October 2017 in the goalless home draw against Internazionale valid for the matchday 9 of 2017–18 Serie A.

[44] In an interview for Albanian media, Hysaj declared that he was invited once by Italian Football Federation but he has refused as he wanted to representing Albania at international level.

[45] After a game against Belarus, three days later he played once more with under-21 against Spain, match valid for qualifying round of 2015 UEFA European Under-21 Football Championship where they lost 2–0.

[48] In this game, at the age of 18, he made his debut, becoming the third youngest player after Blendi Nallbani and Iljaz Çeço to play for the Albania national team.

[60] Hysaj retained his starting place in the Albania's 2018 FIFA World Cup qualification campaign playing three first matches as the full 90-minutes.

[62] On 12 November 2016, in the home game against Israel, Albania suffered a 3–0 loss with the first goal scored by penalty kick conceded by Albanian defender Berat Djimsiti in the 16th minute followed also by a red card and two other goals scored in the second-half after Albania remained now with nine players following another Red card received by Etrit Berisha in the 55th minute after a physical clash against Israeli striker Eran Zahavi, ultimately knocking him down with a headbutt.

Hysaj was substituted off in the 79th minute for striker Edgar Çani as coach Gianni De Biasi placed a trio forwarding line to attempt to score.