Fianna Fáil Senator Mark Daly has been elected Cathaoirleach of the Seanad at its first meeting at the Convention Centre Dublin.
He succeeds Senator Denis O'Donovan in the politically prestigious role.
The Cathaoirleach chairs the Upper House and also represents Seanad Éireann at international meetings.
In the absence or temporary incapacity of the President of Ireland, the Cathaoirleach is a member of the Commission which exercises and performs the powers and functions conferred on the President.
The Cathaoirleach is also a member of the Council of State which aids and counsels the President.
The 60-member Seanad has convened at the Convention Centre, following the formation of the coalition Government and the announcement of the Taoiseach's 11 nominees on Saturday night.
Former Fine Gael minister Regina Doherty will be the leader of the Seanad.
The majority of the Taoiseach's nominees are either councillors, former TDs, or general election candidates from Fianna Fáil, Fine Gael or the Green Party.
However, one Independent nominee, who narrowly lost out in the recent Seanad elections, is the Travellers' rights activist Eileen Flynn, who is now set to become the first female Traveller to ever take a seat in the Oireachtas.
The Taoiseach's 11 nominees are: Regina Doherty (outgoing Fine Gael minister), Timmy Dooley (former FF TD for Clare), Mary Fitzpatrick (FF Dublin councillor), Erin McGreehan (FF Louth county councillor), Aisling Dolan (FG Galway county councillor), Emer Currie (FG Dublin West general election candidate), Mary Seery Kearney (FG South Dublin county councillor), Vincent P Martin (Green Party councillor for Kildare), Róisín Garvey (Green Party councillor for Clare), Eileen Flynn (Travellers' rights activist) and Lorraine Clifford-Lee (FF outgoing senator).
New Senator Eileen Flynn has said that she will be an independent voice for equality in the Seanad - not just for Travellers but for other groups as well.
Traveller activist and new Senator Eileen Flynn has said that she will be an independent voice for equality in the Seanad, not just for Travellers but for other groups as well | Read more: https://t.co/bza8Wunywe pic.twitter.com/dB6S8ZEG5P— RTÉ News (@rtenews) June 29, 2020
On her way into today's sitting at Dublin's Convention Centre, the Travellers' rights activist said she was going to enjoy her first day and take it all in.
She said it was a very emotional day as both of her parents were dead and due to the pandemic, she could not have as good a celebration as she wanted.
On getting the call-up from the Taoiseach, Ms Flynn said it was the best call she ever got in her life and she felt like she was dreaming.
The Senator described it as "phenomenal" that the three party leaders were in agreement to nominate her.
Leader of the Labour Seanad Group, Senator Ivana Bacik, joined her Labour colleagues Senator Annie Hoey, Senator Rebecca Moynihan, Senator Marie Sherlock and Senator Mark Wall for the first session of the incoming Seanad.
Senator Bacik said: "This is an historic day for Seanad Éireann in what has been a truly historic year for Ireland. With women making up nine of the 11 senators appointed by an Taoiseach Micheál Martin over the weekend, 40% of the Seanad is now composed of women.
"While this is a watershed moment for gender equality in Irish politics, it is not cause for complacency. The Seanad figure is not reflected in the abysmal gender breakdown of Dáil Éireann, where only 36 of 160 deputies are women."
The Offences Against the State Act which renews the powers of Special Criminal Court annually was passed which was one of the main priorities of today's sitting.
Meanwhile, the new government has also been criticised for not appointing a Senator from Northern Ireland with a Unionist background.
Former Senator Ian Marshall told the BBC he was "astonished" at this failure, and dismissed a policy commitment by the Government to a "shared island" as a "farce".
A Government source replied that there would be a "major new focus" by the new Coalition on north/south relations, with the establishment of a new unit in the Department of the Taoiseach.
Mr Marshall, a dairy farmer from Markethill in Co Armagh, and an anti-Brexit campaigner, won a seat on the Agricultural Panel between 2018 and 2020.
Reporting Paul Cunningham, Mícheál Lehane