Rough transferred to Hibernian (Hibs) in 1982. Rough was replaced at Hibs by Andy Goram, who had also taken his place in the Scotland squad. After leaving Hibs in 1988, Rough played in the United States with Orlando Lions. Rough also had spells with Celtic (covering for the injured Pat Bonner), Hamilton Academical and Ayr United before leaving senior football.
Rough played in two FIFA World Cup tournaments for Scotland, in 1978 and 1982. He played 53 times for his country, keeping a clean sheet in 16 of those games. At the time of his retirement, Rough was Scotland's most capped goalkeeper, but this record has since been broken by Jim Leighton. Rough's penultimate cap was won in the tragic circumstances of the 1–1 draw with Wales at Ninian Park, Cardiff in 1985. Rough came on as a half-time substitute for Leighton because Leighton had lost his contact lenses. The result, secured by a late Davie Cooperpenalty kick, meant that Scotland qualified for a qualifying play-off against Australia, but managerJock Stein collapsed and died at the end of the match. Rough was selected for the finals by Alex Ferguson, but only played in one further international.
Rough co-presented a football phone-in show on Real Radio Scotland until July 2012, when the station replaced the phone-in with music. From August 2006 to June 2009, the Irish-based sports broadcaster Setanta Sports simulcast the show live twice a week on Setanta Sports 1.
He now co-presents a football phone-in show on Central FM, along with Peter Martin which is shown on STV Glasgow. Rough also writes a column for the Scottish edition of the Daily Mirror.
Rough married Margaret Barry, a Daily Mirror reporter, in 2009 after a seventeen-year engagement. Barry has two children from a previous relationship. Rough was previously married to Michelle, a former model and Tennent's girl. Michelle and Alan had one son, also named Alan.