Access Token for App which accesses a single dropbox account but doesn't require users to login

You should implement the OAuth app authorization flow to let your end-user(s) (in this case, your client) connect their Dropbox account, rather than have them register their own app. It is not possible to get a refresh token (i.e., for long-term access) without doing so.

For reference, we do not recommend having end-users create/register apps themselves on Dropbox and then use the Generate button like this. The developer of the app/plugin/integration should register it once, and then implement the OAuth app authorization flow in the app/plugin/integration so that the end-users can authorize it to access their accounts without having to register and configure it themselves. That would apply to both the previous long-lived access token functionality, as well as the new short-lived access token and refresh token functionality. Previously, the user would need to process the OAuth app authorization flow once to get the long-lived access token. Now, they would do the same, and the app gets a short-lived access token and refresh token the same way, instead of a long-lived access token. The process would look the same to the end-user in both cases. The app would store and re-use the long-lived access token, or the refresh token, respectively.