Spaniard Chirivella joined Liverpool from Valencia as a sixteen-year-old in the summer of 2013. He made an immediate impression and was installed as captain for the Milk Cup in Northern Ireland that year. Despite an injury hit 2014/15 he still managed seven appearances for the Under 21s in domestic competition and five in the UEFA Youth League. In 2015-16 he was included in the party that travelled to Bordeaux for the Europa League game on 17th September 2015 and got an unexpected first-half opportunity when Kolo Toure was forced off through injury. Coming on as a substitute he was slotted into midfield where he put in a composed performance alongside fellow teenager Jordan Rossiter. He came on as a substitute in both FA Cup games against Exeter and made his first start in the fourth round replay at West Ham. On 1st May 2016 he was handed a first Premiership start away to Swansea, but was substituted at half time. After not making the first team at all in the first half of 2016-17, he was loaned to Dutch side Go Ahead Eagles in January to allow him to gain some much needed experience. He scored twice in seventeen appearances but it was not enough to help them avoid relegation. After scoring in Liverpool's opening pre season game of 2017-18 at Tranmere, he was loaned to Dutch top flight side Willem II for the whole of 2017/18 where he made 31 Eredivisie appearances.
As the 2018/19 season approached, Chirivella was clearly not in Klopp's plans but he turned down a move to Norwegian side Rosenborg, with reports stating he hoped to move within England or return to Spain. By the close of the transfer window there had been no offers, meaning he was part of the under 23 set up for at least the first half of the campaign. On 31 January 2019, a deal was agreed that saw him loaned to Spanish second division side Extremedura for the remainder of the season. However a deal in ratifying the paperwork meant he missed the deadline and was unable to play, meaning he had to spend the rest of the season just training there. On 12 June 2020 it was announced that Chirivella will sign a three-year contract with French, Ligue 1 club Nantes once his Liverpool contract expires on 1 July. He was a popular figure at Liverpool and had been offered a new contract at the Reds but he felt he would have a better chance playing regularly somewhere else. Chirivella only featured in six games for Liverpool in the 2019/20 season, solely in cup competitions. He captained a young side at Aston Villa in the Carabao Cup and started FA Cup games at home to Everton and Shrewsbury. Although there was talk of a new deal he was realistic to know his chances would remain limited and he joined Nantes at the expiry of his contract. He became a regular for them over the next two seasons, winning he Coupe de France in 2021/22.