Growing up, Rico's favourite team was Barcelona. His favourite players, past and present, are Alphonso Davies and Jordi Alba. If he was not a professional footballer player, he would have become an athlete of a different sport. His inspiration is his family. Outside of football, he enjoys playing FIFA and Call of Duty. Rico plays as PSG on FIFA. His favourite musical artists include Gunna, Drake, Lil Baby, and Lil Durk. He also enjoys eating steak and Mac and Cheese. Rico's favourite films include Shooter, The Extraction, and American Sniper. In the future, Rico wants to travel the world!

Described by Thomas Frank as one of the best defenders in English football.

Henry joined Walsall at age 11 and progressed through the youth ranks to make his first senior appearance for the club shortly after his 16th birthday, in a pre-season friendly against Leeds United in July 2013. One year later, he signed his first professional contract after impressing for the club's youth team.

Henry made nine appearances during the 2014–15 season, but his progress was disrupted by a dislocated shoulder. He signed a two-year contract extension in April 2015 and was named as Walsall's Young Player of the Year.

Henry broke into the starting line-up on a full-time basis during the 2015–16 season. He had a successful season, making 44 appearances, scoring three goals, signing a new three-year contract and winning England youth international recognition. He was recognised for his performances during the season, being named in the League One PFA Team of the Year and receiving a nomination for the Football League Young Player of the Year award.

Henry made three early-2016–17 season appearances, before suffering a dislocation to the same shoulder previously injured in February 2015 after half an hour of 0–0 draw with Oldham Athletic on 13 August 2016. The Oldham appearance proved to be Henry's last for Walsall and he departed the Bescot Stadium on 31 August. He made 57 appearances and scored three goals for the club.

On 31 August 2016, Henry signed for Brentford on a five-year contract. The transfer reunited Henry with former Walsall manager Dean Smith. He underwent surgery on the dislocated shoulder in September and after returning to fitness, he made his first Brentford appearance on 21 February 2017, making 12 appearances before his season was ended by a knee injury suffered in training in early May.

Henry returned fit for the start of the 2017–18 season, but his season was ended on his eighth appearance by a serious knee injury suffered in a 2–2 draw with Middlesbrough on 30 September 2017. In November 2018, he made his first appearance for nearly 14 months, coincidentally against Middlesbrough, with a late substitute appearance in a 2–1 defeat. He scored his first goal for the club in a 3–1 win over Stoke City on 12 January 2019.

Henry began the 2019–20 season fully fit and signed a new four-year contract in August 2019. He made a career-high 51 appearances during the season, which culminated in defeat in the 2020 Championship play-off Final. He played in almost every game until February during the 20-21 season, when he suffered an injury that would rule him out of the rest of the season, barring one cameo in the Play-Off Semi-Final First Leg at Bournemouth. In his absence, Brentford were promoted to the Premier League with victory in the 2021 Championship play-off Final.

In recognition of his performances during the 2020-21 season, Henry was named in the PFA Championship Team of the Year.

Rico's Premier League debut came on 13 August 2021, when he played in a 2-0 win over Arsenal on the opening day of the season. He finished the season with 37 appearances in all competitions, scoring three goals, as The Bees ended up 13th in the final standings.