Plesk may block the next action or report that the subscription has reached its allowance. The result depends on the limit involved.
A full disk can stop uploads, database writes, backups, and mail delivery. A domain, mailbox, database, FTP account, or subdomain limit prevents another one from being created. A traffic limit can affect site availability if the subscription is configured to enforce it.
Check Statistics and Account > Resources in Plesk. Remove data you no longer need or ask support about a larger plan. Back up files before deleting them.