Walsh, born and raised in Ireland, began his competitive rugby career with Blackrock College in Dublin. The young Scrum Half was a leader on a championship level team, and the school won both the Junior Cup and Senior Cup with Walsh at the helm. He parlayed his performances there into extended looks with the Irish provincial sides.
Between 2009 and 2011, Walsh was a part of the Leinster Under 17s-19s program, and helped the team reach the top of the table every year. His strong form earned him a two-year contract with rival Connacht in 2012. During that time, he also received playing time with Lansdowne Rugby Club, in the All Ireland League, winning the competition in 2013.
In 2014, at the end of his Connacht contract, Walsh moved to Atlanta, Georgia to join perennial powerhouse Life University. He led the team to a National Championship in 2016 as the captain. After earning his degree from the school, Walsh moved to New York City to play for the New York Athletic Club. He has been a contributor, and leader, for the Winged Foot ever since.