Attacking midfielder Palmer and goalkeeper Bazunu, who are both 18, have each signed a two-year extension, taking them through to the summer of 2024.
To help further aid his development, Gavin will also spend the 2020/21 season on loan at League One side Rochdale.
Palmer, who has been at City for more than a decade, was captain of our Under18s side last term, and was in inspired form throughout the 2019/20 campaign.
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He netted a brace in the final of the U18 Premier League Cup, whilst in the league, he scored 15 times and provided five assists in just 14 appearances.
Cole was also voted as the U18 Players’ Player of the Year and following June’s Premier League restart, spent two months training with the first team and was named amongst the substitutes for the first time in our league clash at Chelsea as well as being part of our Champions League squad post the restart.
Bazunu meanwhile moved to City from Shamrock Rovers during the 2018/19 season and has gone from strength to strength ever since.
After making six appearances for our Under 18s and featuring in the squad which reached the 2019 FA Youth Cup final, Gavin was then included in Pep Guardiola’s travelling party for our summer 2019 Asia Tour.
The Ireland Under-21 international was then elevated in the Elite Development Squad for the 2019/20 campaign, making 14 appearances for our Under-23s as well as figuring five times in our UEFA Youth League campaign.
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In a further boost for the Academy, a host of exciting young scholars have signed their first professional contracts with the Club.
Oscar Bobb; Finley Burns; Liam Delap; Samuel Edozie; CJ Egan-Riley; Camron Gbadebo; Joe Hodge; James McAtee; Alex Robertson; Cieran Slicker; James Trafford; Oscar Tarensi and Josh Wilson-Esbrand have all put pen to paper to further extend their stay at the Club.