Morrow becomes a semi-regular with Arsenal in 1992–93. He plays most of his matches in midfield, replacing the injured Paul Davis as Arsenal reaches the League Cup and FA Cup finals. He starts the League Cup final against Sheffield Wednesday. After falling behind to a John Harkes goal, Arsenal equalises through Paul Merson, and then Merson sets up Morrow to score the winner, which is also his first for the club. In the celebrations after the match, Arsenal skipper Tony Adams attempts to pick up Morrow and parade him on his shoulders, but Adams slips and Morrow awkwardly hits the ground. He breaks his arm and has to be rushed to hospital.
As a result, Morrow misses the rest of that season, including the 1993 FA Cup Final, where Arsenal completes the Cup Double. Before the final kicks off, he receives his League Cup winners’ medal.
Morrow is fit enough by the start of the next season but plays only 13 matches, compared to 25 the previous season. One of those is the scene of an Arsenal triumph, the club’s 1994 European Cup Winners’ Cup Final win over Parma. In an Arsenal midfield depleted of John Jensen and David Hillier, he makes his first appearance in the competition that season partnering 20-year-old Ian Selley in central midfield as Arsenal beats Parma 1–0 with an Alan Smith goal.
Morrow nearly leaves the club in March 1994, following an approach from the Premier League‘s bottom club Swindon Town, but the transfer falls through and he signs a new contract with Arsenal, where he spends three more years.
Morrow goes on to play over 20 matches the following season, including a second Cup Winners’ Cup final, which Arsenal loses to Real Zaragoza. He scores his second Arsenal goal in the League Cup once again against Sheffield Wednesday, and scores his first Arsenal league goal in a 3–1 defeat at Blackburn Rovers, who win the Premier League that season. However, he never finds favour under new Arsenal boss Bruce Rioch, who only gives the Irishman five matches in 1995–96.
After the arrival of Arsène Wenger in 1996, Morrow is told he is surplus to requirements at Highbury, and he is loaned to Queens Park Rangers (QPR) in March 1997, the deal being made permanent that summer. He plays 85 games for Arsenal in total, scoring three goals.
At QPR, Morrow is initially a regular, but the club struggles, going from contenders for promotion to the Premiership to facing relegation to the Football League Second Division. Injuries to his shoulder ligaments ruled him out for most of the 1999–2000 season, and he loses his place in the side. He later has a loan spell at Peterborough United, but it does not become permanent, and he is released on a free transfer in the summer of 2001.
Struggling to find a club in the United Kingdom, Morrow moves to the United States to play for Major League Soccer (MLS) side Dallas Burn. He spends two seasons at Dallas, who rename themselves FC Dallas in 2004, before retiring because of a persistent neck injury.
On February 3, 2004, Morrow is named as an assistant coach to FC Dallas but resigns in late May due to personal reasons. However, he returns to the club on January 27, 2005 under coach Colin Clarke. When Clarke is fired on November 7, 2006, Morrow is named interim head coach. On December 11, 2006, FC Dallas removes the ‘interim’ from his title. He is fired as coach on May 20, 2008.
On September 12, 2008 Morrow returns to Arsenal as International Partnerships – Performance Supervisor, managing Arsenal’s international partnerships, which includes the Colorado Rapids of Major League Soccer in the United States, BEC Tero of Thailand and Hoàng Anh Gia Lai of Vietnam, and assisting Arsenal’s academies in countries such as Egypt and Ghana. From 2014, he works as Arsenal’s head of youth development. He leaves Arsenal in 2019 following a coaching staff shake up.
On May 7, 2021, Morrow is appointed The FA’s head of player selection and talent strategy working across England men’s teams.