best way to implement user with trial subscription
In the first place, renewal_date is more an attribute of Account than Institution; so it's in the wrong table. But even further, I would recommend a Subscription entity that would define a many-to-many relationship between Account and Tools.

(Oh. You don't have Tools. Well, maybe you should. You seem to have only one tool. Can you guarantee that will forever be the case?)

Then renewal_date would properly be an attribute of the relationship between Account and the tool they have access to.