Harry Galbreath, also known to his friends as "Harry Love," went to the University of Tennessee, and played for the Volunteers from 1984-87, appearing in every game. He was a starter from his sophomore year on. Coach Johnny Majors remarked that Galbreath was the best run blocker he had ever coached. As a senior in 1987, he was honored with first-team All-SEC and All-American selections. He also won the Jacobs Award, given to the SEC's top lineman annually. He was selected by the Dolphins in the eighth round of the 1988 NFL Entry Draft, 212th overall.
As a rookie, Galbreath appeared in every game, starting 13 at right guard. He helped Miami's running back-by-committee approach gain 1,137 yards between Lorenzo Hampton, Troy Stradford, Ron Davenport and Woody Bennett. Unfortunately, the Dolphins finished 6-10, out of contention.
In 1989, Galbreath appeared in and started 14 games for Miami. The Dolphins running game was still nonexistent, with Sammy Smith the leading rusher with 659 yards on 200 carries. Miami finished 8-8.
1990 would see Galbreath start all 16 games, helping Smith to earn a career high 831 yards on the ground. Miami went 12-4, advancing to the AFC Championship against the Buffalo Bills, losing a 44-34 matchup in Buffalo.
Galbreath again started all 16 games in 1991, as the Dolphins posted a disappointing 8-8 record. Mark Higgs gained 905 yards on the ground for Miami.
Miami would post an 11-5 record in 1992, returning to the AFC Championship game against Buffalo, this time at home at Joe Robbie Stadium. The result was similar to two years before, as Miami didn't have much punch in a 29-10 loss. Galbreath started every game at right guard, as Mark Higgs gained 915 yards.
In total, Galbreath played in 78 games for Miami over five seasons, starting 77 at right guard. He went on to serve as an offensive line coach after his NFL retirement, first with Austin Peay State, later with Tennesssee State, and finally with Hampton University. Galbreath passed away on July 27, 2010.