Revoked access to data within same institute after moving section
Shouldn't the data be usable by another section at the same institute?


Not automatically, without review. 

There are at least two issues. One is that all databases that might have privacy implications should be on a need-to-know basis. Moving around an organization can change what you need to know.

Second, combinations of databases can reveal information that is not stored directly in any of them. An apparently harmless database can help link other data. Letting people keep their old access as they move from section to section increases the risk of someone having a combination of access that has not been properly reviewed.

There is presumably some procedure in your organization for requesting data access. If you still need to access some or all of the data from your old section, use that procedure. If there is no suitable procedure, write up what you need to access and why you need it, and discuss the matter with your supervisor.