Glassey had to wait almost two years before making his first-team debut. The young forward spent much of his time developing with the reserves before being given his opportunity by manager George Patterson during the 1935/36 season. Glassey made a memorable start to his Liverpool career when he scored after just five minutes of his debut against Preston North End at Anfield on 7 December 1935. Liverpool won 2-1, with Glassey's early goal followed by Jack Balmer's late winner. A week later, Glassey scored even earlier, finding the net in the opening minute of Liverpool's 2-1 victory at Brentford.
Glassey's impressive form earned him a regular place in the side for parts of the second half of the season. He scored twice in a 2-2 draw with Middlesbrough at Anfield on 4 April 1936, taking his league tally to four goals. All four of his goals came during the 1935/36 season, when he made eight first division appearances. He also featured against Everton in the Merseyside derby in January 1936, with contemporary reports describing him as a lively and promising young inside-forward.
Glassey's opportunities became much more limited the following season. He made his ninth and final Liverpool appearance at Leeds United on 26 September 1936, his only first-team outing of the 1936/37 campaign. He subsequently suffered a serious leg injury while playing for Liverpool's reserves against Aston Villa on 31 October, which kept him out of football for a considerable period. Liverpool eventually released Glassey in 1937. He returned to Horden Colliery Welfare before attempting to revive his professional career with Stoke City, but didn't make a first-team league appearance for the club. He later moved to Mansfield Town, where he made three Football League appearances and scored once during the 1939/40 season.
