Leyton Orient 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. He scored his first senior goal in his next game, the 4–0 win at
Newport County on 4 March 2017.
Brighton & Hove Albion On 31 July 2017, Alzate signed for
Brighton & Hove Albion for an undisclosed fee.
Loan Swindon Town On 2 July 2018, Alzate joined
League Two side
Swindon Town on a season-long loan. His first goal for the club came on 22 September, against
Yeovil Town, when he scored with a 20-yard strike. On 1 January 2019, Alzate was ruled out for at least three months after he was diagnosed with a stress fracture to his back. The loan deal expired on 9 January, and Alzate returned to Brighton.
Breakthrough at Brighton 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. 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. 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. He made his home debut on 5 October where he started the match against
Tottenham Hotspur, which ended in a 3–0 victory. 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. 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. 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 in a league game for the first time since 1989. 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. He was later ruled out for three months with an ankle injury. 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. Alzate made his first league start of the season where he played the whole of the 1–1 home draw against
European champions Chelsea on 18 January 2022. 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. On 5 June 2024, Brighton announced that Alzate would be leaving the club at the expiration of his contract in the summer, ending his seven-year spell with the Seagulls.
Loans to Standard Liège On 9 September 2022, Alzate signed for
Belgian Pro League side
Standard Liège on loan for the
2022–23 season. On 6 September 2023, Alzate re-signed with the club on a loan deal for another season.
Hull City On 9 September 2024, Alzate signed for
Hull City on a two-year deal, with an option for a further 12 months. ==International career==