Gibbons first joined Port Vale at the age of 11, though by the age of 15 coaches questioned whether he would make it in the game due to his small stature. He did however go on to turn professional at the club in April 2016. He joined Northern Premier League Division One South club Leek Town on a one-month loan on 17 September 2016, and made his debut for the club later that day in a 2–1 defeat to Sheffield. He made a total of five starts for the club. He made his senior debut for the "Valiants" as a 60th-minute substitute for Paulo Tavares in a 4–0 victory over Hartlepool United in an FA Cup tie at Vale Park on 4 December 2016. He signed a new one-year contract in May 2017. He did not make a first-team appearance under manager Michael Brown, but was selected by caretaker-managers David Kelly and Chris Morgan for his EFL League Two debut on 23 September 2017, and was sent off after receiving two yellow cards during what ended as a 1–1 draw at Yeovil Town. New manager Neil Aspin said that "I don't look at him as a young lad, I just look at him as a player. He is a player who deserves to be playing and I am happy with him." He signed a two-year contract extension in November to keep him at the club until 2020. He was sent off for the second time in his career on 12 December, again away at Yeovil, for committing a dangerous challenge; he was handed a four match suspension. However Aspin heavily criticised referee Gavin Ward, and said "there is no criticism from me in this instance because he is a competitive player and we want to keep that". Gibbons returned to the starting eleven after serving his suspension, and though the defensive line-up changed due to the departures of Gavin Gunning and Tom Anderson he refused to accept any excuses for what he admitted was a decline in the team's form and his own personal performances. He was named as the club's Young Player of the Year at the end of the 2017–18 season. He started the 2018–19 season in the starting eleven at right-back, and had only teenage loanee Mitch Clark as competition. However he found himself out of the starting eleven as Aspin felt he was too inconsistent. A hip injury then saw him sidelined for a month. On 29 January 2019, he was sent off for the third time in his career during a 0–0 draw at Newport County, but the club successfully appealed the red card. He made the last of his 19 appearances of the season in a 1–0 defeat at Cheltenham Town on 23 February. He started the 2019–20 season as new manager John Askey's first-choice right-back, ahead of new signing Callum Evans. He did, however, pick up five yellow cards in the league before October and was given a one match suspension, leading to Askey to criticise him for picking up "daft bookings". After a public vote held in December 2019, he was named by The Sentinel as Port Vale's second-best right-back of the 2010s with 27% of the vote, behind Adam Yates and ahead of Ben Purkiss. On 14 January, he scored his first goal in professional football during a 2–1 defeat at Morecambe. It was revealed the next month that the club had an option to extend his contract beyond the summer. However he instead signed a new contract to keep him at the club until summer 2022.
Style of play
Gibbons is a right-back, though can also fill in at left-back, and has been described as a "little terrier" by former manager Rob Page. Port Vale youth coach Mick Ede compared his style to that of Mike Pejic, saying that "he plays with a lot of intensity and physicality". His physicality has led to a poor disciplinary record and therefore suspensions, though Gibbons commented that "you are not going to win every tackle so it is going to happen". He is also adept at going forward and delivering crosses.