As a young man Hannigan began performing at festivals and local events, playing the Uilleann pipes, tin whistle and percussion instruments. In 1991 he and Simon Care performed the soundtrack for a BBC radio play, Voyage of the Swallows, by Eric Pringle. In 1992 he won an All-Britain Uillean pipe award. In 1994 he published an instructional book, Bodhrán Basics
Hannigan founded the Steafan Hannigan Band, which later became the Irish band Sin É. The band released two albums, Sin É and It's About Time. The group performed internationally, including at Lincoln Center in New York in 1997. Hannigan opened Oisin Studios in Milton Keynes, England, and produced a number of albums, including Tig (Serious Kitchen), and Not to Scale (Kerfuffle). While there he was interviewed by Irish Music Magazine in 1999.
In 1999, Hannigan and Sin É released an album in the United States, Deep Water Dropoff on the RCA label.
As well as fronting his own band, Hannigan performed widely with other artists and bands, including Depeche Mode Bjork, Aessia D'Andrea, and Band of Hope. He played various instruments on the albums of many bands and singers (see the discography section below).
In 2000 he published another instructional book, The Low Whistle Book, with David Ledsam.
Hannigan met and married violinist Saskia Tomkins. In 2008, after moving to Canada, Hannigan and Tomkins formed a band called Cairdeas (Friends) with singer Elizabeth Barlow, and independently released an album of Irish songs and tunes, Generous Lover. Barlow was later replaced by Marsala Lukianchuk, and the band released a second album, Christmas by Candlelight. The pair continued to perform both together and separately with various Canadian groups.
During his career Hannigan has performed and presented workshops at many festivals and other music-related venues.
In 2011 Hannigan performed The Brendan Voyage, by Shaun Davey, the only classical suite written especially for uilleann pipes, accompanied by the Northumberland Orchestra in Cobourg. Hannigan was the sound editor and audio effects creator for the 26 part animated film series Legend of Ponnivala, released in 2013. In 2014 he created an original score for the Capital Theatre production of Driving Miss Daisy in Cobourg.