Julie here from Shopify Support.
As a Shopify Partner, you can use either the REST Admin API or GraphQL Admin API to bill merchants for your app.
In the REST Admin API help documentation, there is a section on extending free trials. There, you'll see that it's not possible to extend an existing free trial. Instead, you can cancel the charge that the trial is associated with and issue a new charge.
We also have help documentation for billing with the GraphQL Admin API. While you'll find some information on free trials there, it doesn't indicate whether trial extensions are possible. I got in touch with our Partners team for more information and they confirmed that like the REST Admin API, it is not possible to extend trials.
Our Partners team suggests canceling the charge and recreating it. You can also choose to reset free trials if merchants uninstall and reinstall your app, which may be another workaround worth considering. You can learn how to do this here.
I hope this helps! What kind of app do you have?