In Gaelic football Noonan has a long association with the Nemo Rangers club and she won All-Ireland medals with Cork at under-14, under-16, and minor level.

In November 2020 the Republic of Ireland soccer manager Vera Pauw said of Noonan: "Playing two sports and just being so natural and so clinical about it is amazing".

[8] In 2017 Noonan was named the WNL Young Player of the Season,[9] and helped rapidly-improving Cork City win their first major trophy by beating UCD Waves 1–0 in the final of the FAI Women's Cup at the Aviva Stadium.

[12] In the final match of the league season against Peamount United, she suffered a partially torn anterior cruciate ligament which did not require surgery but ruled her out for around five months.

[13] Cork City finished fifth of eight teams to equal their best performance, but Noonan – the club's all-time record goal scorer – was sometimes unavailable due to her Gaelic football commitments.

[15] She started the season in good form and was praised by Cork City's coach Ronan Collins after she won the September 2020 Player of the Month award: "Saoirse has loads of ability and talent, but sometimes we forget how young she is as she only turned 21 recently.

[18] Noonan's continued good form made her a transfer target for professional foreign clubs including Víkingur FC, Aston Villa and London City Lionesses.

[23] On the final day of the January 2022 transfer window, Noonan agreed to join FA Women's Championship club Durham WFC.

Noonan continued with the under-17 national team and in March 2016 was the captain when they competed at the 2016 UEFA Women's Under-17 Championship qualification elite round in France.

[41] In August 2016 Ireland coach Susan Ronan named Noonan in a young and predominantly home-based senior squad for a training camp in Wales.

[46] In October 2020 it was reported that Noonan's good form for Cork City had brought her to the attention of Ireland's senior national team coach Vera Pauw.

[47] Under Pauw's predecessor Colin Bell Noonan had been restricted to the "fringes", but still attended national team training sessions for home-based players and still harboured ambitions of playing for Ireland.

[48] Pauw gave Noonan her first competitive appearance for Ireland in the opening 2023 FIFA Women's World Cup qualification – UEFA Group A fixture against Sweden at Tallaght Stadium on 21 October 2021.

[50] In her early childhood Noonan began playing Gaelic football at the Nemo Rangers club, where her father was one of the coaches and her brother was a player in the youth system.

[52] Noonan's potential was noticed by county selectors and in 2013 she won Munster and All-Ireland Under-14 Ladies' Football Championship titles with Cork's under-14 panel.

[46][32] She was an immediate success at minor level, making her debut in a May 2016 victory over Kerry in the Munster final,[32] playing against Galway in the All-Ireland semi-final and scoring one goal and 11 points across these first two appearances.

[55][56] She acquired a reputation as a prolific "super sub" by adding 4–9 in four more substitute appearances as Cork qualified for the 2018 All-Ireland Senior Ladies' Football Championship final.

[12] Despite a partially torn anterior cruciate ligament sustained playing soccer in November 2018, Noonan's good form continued into the 2019 Gaelic football season.

[46][6] In October 2019 Noonan was one of three Irish women to attend an AFL Draft Combine in Melbourne, but she was unable to participate in the tests due to a knee injury.