Well, they get it regardless. If they inject themselves with something unsanctioned then yes the clubs can break the contracts probably, but the league and state is demanding or encouraging the vaccination. If the contract is short and lawyers can prove that heart injury is linked to the vaccine then they could sue the league or club for further damage concerning the athlete's lost earnings over his career. The big money long term contracts are reserved for the best players in US sports. I don't think European soccer clubs sign more than around 4 years. Players don't want it because of wage inflation and if they improve then they can demand more money.

The first major international case in all this, Eriksen from Denmark in June 2021 at the Euros, is still mum about his vaccine status. It must be because he was vaccinated even though the national federation had declared that they could not jump the queue in July, so the Danish national team overall was officially not vaccinated. But his club doctor or president was quoted as saying that "everyone is vaccinated" in May 2021.