Pappoe joined Chelsea as a schoolboy at under-12 level. He featured for the Chelsea reserves during the 2009–10 season while still studying at school, and was an important member of the FA Youth Cup-winning squad of 2010, though he missed the final through injury. Pappoe captained the 2010–11 FA Youth Cup side, but missed the end of the campaign through injury, additionally playing nine reserve games, but was sent off against Blackpool after lashing out at an opponent. He missed the start of the 2011–12 season with injuries, returning in early 2012, only to suffer another serious injury, where he was ruled out for the remainder of the season. He returned to action with the youth and reserve teams part-way through the 2012–13 season, and featured in the semi-final and final of the 2012–13 NextGen Series, where the Blues finished as runners-up to Aston Villa.
Loan spells
Yet to make his Chelsea first-team debut, Pappoe signed on loan with League One club Colchester United on 16 July 2013, teaming up with fellow Chelsea youth-team product Sam Walker in his second loan-spell with the U's. He made his professional debut as an 86th-minute substitute for Alex Gilbey in a 2–2 draw with Bradford City on 14 September. However, just four minutes after coming on, he was given a red card for a tackle on former Colchester player Mark Yeates, becoming the seventh United player to be sent off on their debut. On 31 October 2013, Pappoe's loan at Colchester was terminated due to his opportunities being limited. Following Pappoe's unsuccessful loan spell at Colchester United, he joined Isthmian Premier League side Kingstonian on a one-month loan deal.
Post Chelsea career
On 4 August 2014, Pappoe along with former Chelsea teammate George Cole, joined the development squad of Brighton & Hove Albion signing a one-year deal. However, on 30 June 2015, Pappoe was released at the expiry of his short-term deal without making a single appearance for Brighton. On 25 October 2015, Pappoe joined Isthmian Premier Division side Hampton & Richmond Borough on a non-contract deal. However, after failing to make an appearance under manager Alan Dowson, Pappoe left the club. On 19 December 2015, Pappoe joined National League South side Hemel Hempstead Town on a short-term deal. On the same day, Pappoe made his Hemel Hempstead Town debut in a 2–0 victory over Oxford City, playing the full 90 minutes. After only making four more appearances, Pappoe made the switch to German side Berliner AK 07. Although after making only making one appearance, Pappoe returned to England to re-join Hemel Hempstead Town, where he went onto make only four more league appearances. On 9 August 2016, Pappoe joined League Two side Crawley Town on a non-contract basis, re-uniting with former Chelsea Reserves and Academy manager Dermot Drummy. On 4 October 2016, after almost two months after signing for Crawley, Pappoe was given his debut in a 2–0 victory over Charlton Athletic in an EFL Trophy tie, replacing Mark Connolly with eight minutes remaining. On 11 January 2017, Pappoe joined Maldives-based side New Radiant, after failing to impress at Crawley. However, after three weeks of his arrival in the Maldives, his contract with New Radiant was promptly rescinded and he was given ten days notice after the club assessed his performance as poor. It was also confirmed that he had a pre-existing knee injury that he had failed to declare pre-transfer. On 22 August 2017, Pappoe joined Romanian side Foresta Suceava although doubts about his fitness status still remain. Pappoe had been playing for Carshalton Athletic from 15 September to 16 December 2018 on loan from Dulwich Hamlet. However, on 28 January 2019, he signed permanently for Carshalton Athletic.
International career
In 2013, he represented Ghana U20 in the four-team Valais Youth Cup. He played in games versus Kosovo and Brazil. He was initially named in the FIFA U-20 World Cup squad but was later replaced with Israel-based Baba Mensah.