The phrase "conditional approval" means that something or someone has been approved, but there are certain conditions or requirements that still need to be met. Full definition
You can become a member now or following conditional approval of your loan application. (cportcu.org)
A two (or more) stage process, with conditional approvals at each step is the only practical manner to implement a project of this magnitude. (slaw.ca)
Application conditional approvals may take up to 10 business days. (pentagonfoundation.org)