Alzate made his Football League debut as a second-half substitute for Sandro Semedo in Orient's 4–1 defeat at Stevenage on 28 February 2017.[3] He scored his first senior goal in his next game, the 4–0 win at Newport County on 4 March 2017.[4]
On 2 July 2018, Alzate joined League Two side Swindon Town on a season-long loan.[6] His first goal for the club came on 22 September, against Yeovil Town, when he scored with a 20-yard strike.[7] On 1 January 2019, Alzate was ruled out for at least three months after he was diagnosed with a stress fracture to his back.[8] The loan deal expired on 9 January, and Alzate returned to Brighton.[9]
Alzate made his debut for the "Seagulls" in the EFL Cup on 27 August 2019 where he played the full match in the 2–1 away win against Bristol Rovers setting up Glenn Murray's late winner.[10] Alzate was named on the bench in a Premier League fixture for the first time in a 1–1 home draw against Burnley on 14 September. He remained an unused substitute.[11] Alzate made his Premier League and league debut for Brighton on 21 September playing the full match in the 0–0 draw at Newcastle United.[12] He made his home debut on 5 October where he started the match against Tottenham Hotspur, which ended in a 3–0 victory.[13]
Alzate scored his first Albion goal on 23 January 2021, deflecting a Alexis Mac Allister shot in the back of the net in a 2–1 home victory over Blackpool in the FA Cup fourth round, a match where he also recorded an assist for Yves Bissouma's 30-yard stunner.[14] On 3 February 2021, Alzate scored his first Premier League goal to secure a 1–0 away win over Liverpool, sealing Brighton's first win at Anfield in Premier League history and their first league win at Liverpool since 1982.[15] Alzate played in Brighton's 3–2 home victory over champions Manchester City on 18 May, with fans returning to football, in which they went from 2–0 down to beat City for the first time since 1989.[16]
Alzate made four appearances at the start of the 2021–22 season suffering an injury on his fourth appearance in the 1–1 away draw against bitter rivals Crystal Palace on 27 September, replacing the injured Dan Burn at half time before coming off injured himself 20 minutes later.[17] He was later ruled out for three months with an ankle injury.[18]
He made his return to action on Boxing Day, coming on as a substitute and helping Brighton maintain their lead in the 2–0 home victory over Brentford.[19] Alzate made his first league start of the season where he played the whole of the 1–1 home draw against European championsChelsea on 18 January 2022.[20]
Alzate scored a long distance effort in his first game of the 2022–23 season on 24 August 2022, scoring Brighton's second in the eventual 3–0 away win over League One side Forest Green Rovers in the second round of the EFL Cup .[21]
On 6 November 2019, Alzate received his first call-up to the Colombia national team for friendlies against Peru and Ecuador in November 2019.[25] He made his debut on 16 November coming on as a substitute in a 1–0 home victory over Peru.[26] Five days later he made his first start for Colombia in the 1–0 away win against Ecuador where he was highly praised by manager Carlos Queiroz.[27]
Alzate was recalled to the Colombia squad in January 2022 for 2022 FIFA World Cup qualifiers against Peru and Argentina, after not being included in selection since October 2020.[28]
