Youth career Murphy began playing with his local side Donnycarney United before moving to top
Dublin academy
Belvedere where he played from U8 to U15 level where he impressed
League of Ireland club
St Patrick's Athletic to sign him in January 2020. He initially captained the club's U15 side before quickly moving up through the U17 and U19 sides. He was called up to train with the first team at aged 15 during 2021 after the club had opted to pay for private schooling for him at
The Institute of Education in order to allow him also train during the mornings. On 20 October 2021, Murphy captained the club's U19 side away to
Crvena Zvezda in the
UEFA Youth League. He was part of the side that won the
League of Ireland U19 Division in 2022. In February 2023, Murphy featured in a
Sky News report on how young Irish footballers career paths have been impacted by
Brexit.
St Patrick's Athletic 2021 season Murphy signed his first professional contract with
St Patrick's Athletic on 7 July 2021, alongside
James Abankwah. He was named on the substitutes bench for first team games away to
Bohemians in July 2021 and at home to
Dundalk in October 2021.
2022 season Murphy's senior debut came on 25 February 2022 when he replaced
Billy King in the 85th minute of a 2–1 loss at home to
Sligo Rovers. His first start at senior level came on 8 April 2022, his 17th birthday, in a 0–0 draw at home to
Dundalk in which Murphy impressed in the opening 21 minutes before being forced off with a hamstring injury that would require surgery and keep him out of action for almost the entirety of the rest of the season. That start made him the youngest player to start a game for the club in the modern era at the time (the feat has since been taken by
Sam Curtis). His return from injury came on 6 November 2023 in the final game of the season, a 4–0 win over
Shelbourne.
2023 season Murphy picked up an injury during pre-season for the
2023 season which delayed his progress at the start of the season, having to wait until 17 March 2023 for his first league appearance of the season when he came off the bench against
Shamrock Rovers to provide an assist for
Jake Mulraney's 89th-minute equaliser in a 2–2 draw at
Tallaght Stadium. His first start of the season came on 14 April 2023, in a 3–2 win away to
Bohemians, with manager
Tim Clancy stating after the game that ''"From anywhere I've played or managed, he's the best young kid I've ever seen. I rate him that highly, he's exceptional, a really good player."'' On 5 May 2023, Murphy scored the first goal of his senior career, coming off the bench at half time to score the winning goal in a 3–2 win away to
Cork City at
Turners Cross. On 12 July 2023, Murphy made his first appearance in European competition in a 2–1 loss against
F91 Dudelange in the
first qualifying round of the
UEFA Europa Conference League at the
Stade Jos Nosbaum. On 20 July 2023, Murphy gave his side a 2–1 lead on the night in the return leg against
F91 Dudelange, before his side eventually lost out 3–2 at
Richmond Park. On 23 July 2023, Murphy scored his second goal in 4 days when he opened the scoring in a 2–1 win away to
Longford Town in the first round of the
2023 FAI Cup. His form in July saw him voted as the club's Player of the Month and in August 2023, he was subject to a bid from
EFL Championship club
Bristol City, which was turned down. On 12 November 2023, Murphy came off the bench in the
2023 FAI Cup Final, in a 3–1 win over
Bohemians in front of a record breaking
FAI Cup Final crowd of 43,881 at the
Aviva Stadium.
Bristol City On 3 January 2024, Murphy signed for
EFL Championship club
Bristol City on a three-and-a-half-year deal with an additional 12-month option. Murphy's first 18 months at the club were severely hampered with injury issues, meaning he had to wait until 9 August 2025 for his first involvement in a matchday squad with the first team, in which he was an unused substitute in a 4–1 win away to
Sheffield United.
Swindon Town loan On 1 September 2025, Murphy signed for
EFL League Two side
Swindon Town on a season long loan deal. He made his debut for the club on 13 September 2025, in a 3–1 win at over
Harrogate Town at
The County Ground. He made 5 appearances for the club before on 9 January 2026, it was announced that his loan spell had been cut short due to an ankle injury suffered in training, with Swindon manager
Ian Holloway stating ''"I feel for him, I really do. I really liked him. I think he's really going to make himself a player. Would I have him back here? All day long, fantastic lad. But unfortunately, injuries happen, so yes, he won't be coming back."'', before he returned to his parent club to continue his rehabilitation on the injury. ==International career==