Poblete started his senior career in 2011 with Argentine Primera División side Colón, he was an unused substitute four times during the 2011–12 season.[1] He made his professional debut on 16 February 2014 in a game against Argentinos Juniors.[3] In his next appearance versus Argentinos Juniors, in September 2014, Poblete scored his first goal for Colón in a 0–2 win.[1] In total, Poblete made seventy-three appearances and scored two goals in his first six seasons with Colón, twenty of those appearances and one of those goals fell during the club's 2014 season in Primera B Nacional following relegation in 2013–14 to the country's second tier.[1]
On 4 July 2017, after one hundred and seven appearances for Colón, Poblete departed to France to join Ligue 1 club Metz.[1] He joined on a free transfer and signed a four-year contract.[6] Poblete's Ligue 1 debut came on 5 August versus Guingamp, he played the full match in a 1–3 defeat.[1][7] On 11 August 2018, San Lorenzo loaned Poblete.[1] Twenty-two appearances followed in 2018–19.[1] Poblete left San Lorenzo on 30 June 2019, but returned on a fresh loan deal on 21 July.[8][9][10] He made another twenty-two appearances.[1] Poblete returned to Metz in June 2020, subsequently featuring twice for their reserve team in Championnat National 2.[1]
Poblete terminated his Metz contract on 29 October, prior to returning to South America with Chilean Primera División team Deportes La Serena.[11] He made his debut on 15 November in a home win over Huachipato, which preceded fifteen further appearances in 2020 as the club finished fifteenth; avoiding the relegation play-off due to goal difference and relegation itself by one point.[1] On 19 February 2021, Poblete went back to his homeland with Vélez Sarsfield.[12][13]
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