A more case-law-based answer:
The IHR [International Health Regulations (2005)] contains a dispute settlement provision, so a state party could advance legal claims that China violated the IHR and, under principles of state responsibility, has an obligation to make reparation for the damage caused by that wrongful act. However, countries have never used the dispute settlement provisions in infectious disease treaties from the nineteenth century through today — another indication that states have no interest in legal remedies in this area. [...]
Any pursuit of a claim against China under the principles of state responsibility would also have difficulty with the causation element of those rules. The [UN] International Law Commission has explained that the causation requirement focuses on “the injury from and ascribable to the wrongful act, rather than any and all consequences flowing from an intentionally wrongful act.” Thus, whatever reparation China might owe under these principles likely does not encompass the trillions of dollars of damage associated with the outbreak. What’s more, as commentary has noted, many countries now struggling with COVID-19 had time to prepare for the pathogen’s transboundary spread after China reported its outbreak under the IHR. Under the principles of state responsibility, separating what damage is attributable to China’s delayed reporting and what harms arose because other governments botched their responses to COVID-19 would be difficult. Such causation issues also help explain why states have, historically, not pursued reparations for damage associated with alleged violations of treaties on infectious diseases.
Note that this strictly from an international law perspective. There are several efforts in the US to sue China domestically, under US law, lawsuits which are mostly hampered by FSIA. (But there is precedent in bypassing that by Congressional amendment in the case of lawsuits against Saudi Arabia for 9/11 [JASTA] and there are some similar amendments being advanced now, targeting China.) I won't get to the details on that here since you commented that "I am thinking more in terms of international-law".
Outside of that realm of lawsuits, Trump has recently (sort of) threatened China with more sanctions for Covid-19:
“We signed a trade deal where they’re supposed to buy, and they’ve been buying a lot, actually. But that now becomes secondary to what took place with the virus,” Trump told reporters. “The virus situation is just not acceptable.” [...]
Asked whether he would consider having the United States stop payment of its debt obligations as a way to punish Beijing, Trump said: “Well, I can do it differently. I can do the same thing, but even for more money, just by putting on tariffs. So, I don’t have to do that.”
As with all such [tariff] measures, there could be tit-for-tat retaliation from China.
Also, both Congress and the administration seem somewhat divided on how exactly to punish China, so immediate action is not expected. (On that [speed-of-action] note, the lawsuits against Saudi Arabia for 9/11 are still, slowly making their way through the US courts. So even if those against China were allowed to proceed, they probably won't be over quickly. On the other hand, tariffs could be [re]imposed fast.)