Federico Chiesa (Juventus to Liverpool, £10m)

For many Liverpool fans the summer window was too quiet, with no major arrivals and contracts left unsigned. Arne Slot’s impressive start has eased frustrations, and the Valencia keeper Giorgi Mamardashvili has agreed to join next summer – but when a new face arrived at Anfield, he was undeniably a bargain. Chiesa was frozen out at Juventus and has had issues with form and fitness, but he has the skillset to succeed in the Premier League and is still only 26. Birmingham City paid £5m more to sign Jay Stansfield from Fulham on deadline day. Chiesa need offer only glimpses of his best to repay his cut-price fee.

Khéphren Thuram (Nice to Juventus, £17.1m)

Last summer, Nice’s driving force in midfield was linked with several Premier League clubs – but Thuram struggled in Francesco Farioli’s conservative system last season and slipped off a few radars. Juventus were never likely to forget about him; his father, Lilian, is a club legend who joined Juve in 2001, the year Khéphren was born. The Italian giants moved quickly to sign a player with one year on his contract, and he could spark a sibling rivalry for the scudetto with his brother, Marcus, who is at Inter. He started Juve’s season opener against Como but sustained a minor injury. When he returns, he will add necessary steel to Thiago Motta’s reshaped midfield.

Alejandro Francés (Zaragoza to Girona, £3m)

Although Francés had spent his entire career in his home town until late July, he was known far beyond Spain’s second division. Ever since his Copa del Rey debut at the age of 19, the skilful centre-back has been linked with La Liga sides including Barcelona, Real Madrid and Sevilla. Francés opted to stay put and refine his game across 123 league appearances with Real Zaragoza. This summer, Girona came calling and the timing and destination felt right for the now 22-year-old: “Girona is growing a lot and I want to grow with them.” The learning curve may be steep, with a tough Champions League fixture list to come and the head coach, Michel, who seeks versatility from his players, giving Francés his first two starts at right-back.

Ismaïla Sarr (Marseille to Crystal Palace, £12.5m)

Crystal Palace face a perpetual battle to keep hold of their best players but decided to quickly concede in the case of Michael Olise, who left for Bayern Munich in early July. Two weeks later, Oliver Glasner had a replacement winger for a quarter of the €60m banked for Olise, as Sarr returned to the Premier League and took the No 7 shirt. The former Watford winger may not be as imposing or magnetic a player as Olise but he looks a good fit for Glasner’s system and freed up funds for further signings. Palace have started slowly but Sarr caught the eye off the bench in the 1-1 draw at Chelsea and will be aiming to hold down a starting place after the international break.

Luka Sucic (Salzburg to Real Sociedad, £8.5m)

It was a mixed window for Real Sociedad, who lost Robin Le Normand to Atlético Madrid and Mikel Merino to Arsenal but persuaded Martín Zubimendi to turn down Liverpool. Along with making sensible depth signings such as the Manchester City auxiliary man Sergio Gómez, La Real splashed more than £25m on two young talents, the bulk of that spent on the prolific but raw Icelandic striker Orri Óskarsson. The £8.5m spent to sign the Croatian playmaker Sucic looks less risky. The 21-year-old brings useful European experience, with 22 Champions League appearances. With only a year on his contract, a player who has earned inevitable Luka Modric comparisons was courted by Liverpool, Juventus and more this summer – but Real Sociedad convinced him La Liga was the right next step.

Samuel Dahl (Djurgården to Roma, £3.4m)

From playing in the Swedish second division with Örebro just over a year ago, Dahl has enjoyed a stratospheric rise. After impressing at full-back and further upfield, he was snapped up by Djurgården for less than £250,000 in July. Initially regarded as a cheap backup to another new signing, Rami Kaib, Dahl quickly made the left-back place his own – and after 12 months in the Swedish top flight, the 21-year-old has joined Roma for about 14 times the fee Djurgården paid. Dahl’s composure and consistency belie his age and earned him an international callup in January. He will not start as the first-choice left-back for the giallorossi, but that has not held him back before.

Léo Scienza (Ulm to Heidenheim, £420,000)

It has been a long road to the top of the Bundesliga for Scienza, whose career took him to Chapecoense, Uruguay and the Swedish fifth tier before he was picked up by Schalke. Despite turning heads with their second team, the Brazilian winger was moved on to Magdeburg then, in Germany’s third division, SSV Ulm. It was there that Scienza finally found his groove, scoring 12 goals and setting up 15 to lead the team to promotion. Heidenheim, who have lost their top scorer, Jan-Niklas Beste, to Benfica, swooped to sign Scienza for €500,000. He has made an immediate impact, scoring in the 4-0 win over Augsburg that took Heidenheim top of the Bundesliga. Like his new club, Scienza has a knack for defying the odds.

Jorge Cuenca (Villarreal to Fulham, £5.7m)

Fulham signed six players this summer, five of them familiar names from other English clubs who can expect to slot into Marco Silva’s starting XI. The outlier is Cuenca, a defensive recruit whose arrival prompted one Fulham fan blog to ask: who the heck is Jorge Cuenca? Well, he’s a left-sided centre-back who emerged from Barcelona’s academy and became a regular at Villarreal last season. Cultured on the ball and versatile enough to slot in at left-back, he made a solid debut in the Carabao Cup. Cuenca may not be the most dazzling of Silva’s recruits but he could prove to be the best investment.

Leopold Querfeld (Rapid Vienna to Union Berlin, £2.5m)

After finishing fourth in 2022-23, Union Berlin fell away last season, avoiding the relegation playoff on goal difference. With European football adding to their schedule, the squad’s average age – 27.6, the second-oldest in the league – proved a hindrance. Union have targeted fresher faces this summer including Querfeld, a 20-year-old centre-back who was the youngest member of Ralf Rangnick’s impressive Austria squad at Euro 2024. Querfeld appears to have the strength – he is from a rowing family – and intelligence to succeed at a higher level. His former club describe him as “exceptionally mature … a role model”.

Theo Bair (Motherwell to Auxerre, £1.4m)

Thelonius Bair (to use his full name) was plucked from the youth leagues of his home town, Ottawa, by the Vancouver Whitecaps in 2019. Despite a promising start to his MLS career, the centre-forward’s progress stalled and after a loan spell in Norway, he was allowed to join St Johnstone. After one goal in 34 appearances, Bair’s contract was terminated and expectations were low when he joined Motherwell last August. Bair proved to be an unexpected hit, scoring 15 goals and catching the eye of the Ligue 1 returnees Auxerre after a season at Fir Park he described as “unbelievable”. It also boosted his international career as he earned a spot in Canada’s Copa América squad.