Ms. McDonald’s accession in the tightly disciplined party — she was the only candidate — would appear to swing the political center of gravity of Sinn Fein, the only major party organized in Ireland and Northern Ireland, back to the south after decades of northern domination.
While she has attempted to boost her party’s prospects in the south, the northern branch of the party, led by Michelle O’Neill, 41, who was installed as Sinn Fein’s vice president on Saturday, is in a standoff with its chief rival, the Democratic Unionist Party.
That led to the collapse of a power-sharing administration last year. Attempts to resolve the impasse, and avoid the reintroduction of direct rule from London, appeared to make progress last week.
Although Sinn Fein has in recent years used a strong roster of candidates to build electoral support in the Republic of Ireland, some southern voters who would otherwise be attracted to its broadly center-left policies are still troubled by its previous support for I.R.A. violence under Mr. Adams’s presidency.
Mr. Adams has always denied having been in the I.R.A., but several former republicans have claimed that he had been an active service member in West Belfast in the 1970s and rose to command the organization as chief of staff in 1977, at the height of its violent struggle to end British rule in Northern Ireland.
About 3,500 people died in the Troubles between 1969 and 1998, with the republican side, dominated by the Provisional I.R.A., believed to be responsible for more than 2,000 of these deaths.
Victims of the mainly Roman Catholic I.R.A. included British soldiers, Northern Ireland police officers and Loyalist terrorist opponents, but also many civilian members of the mainly pro-British Protestant majority in Northern Ireland and numerous Catholic civilians who opposed the I.R.A. or were accused of being informers or collaborators.
Mr. Adams has been accused of personally ordering the killings of some of those suspected of being informants. He was questioned in 2014 about the disappearance of Jean McConville, 38, a widowed mother of 10 who was abducted by I.R.A. gunmen in 1972 and found buried on a beach in 2003. He has strongly denied any role in her death and was released without charge.
His successor carries no such historical baggage. Born in a middle-class Dublin neighborhood, Ms. McDonald joined Sinn Fein after the 1998 peace agreement, having previously belonged to Fianna Fail, a conservative establishment party. She is a formidable and aggressive debater, respected by opponents for her communication skills and her grip on policy details.
Founded in Dublin in 1905, Sinn Fein has gone through several splits and reinventions to survive as the oldest brand in Irish politics.
Diarmaid Ferriter, a historian at University College Dublin, said Mr. Adams would be remembered as a ruthless pragmatist who had taken part in the escalation of violence in the 1970s, then led the long retreat from armed struggle that began in the 1980s while avoiding major splits.
“I don’t think there was anyone else who could have kept the republican movement united during the peace process, and that is a pretty big legacy,” Professor Ferriter said.
Mr. Adams retains his seat in the Dublin Parliament and may contest it again at the next election. In a recent blog post he wrote: “In their rush to write my political obituary, some in the media have concluded that I’m now to retire. Well, they’re wrong. I will continue to serve the republican struggle and Sinn Fein, if and when I can.”
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