Accessing data from an outsourced third party service company

Hi , Can someone please throw some light on this ?

We have some services outsourced to a third-party company but, we realised the data which goes into their process is very valuable and want to access it for different purposes. 

we are currently downloading certain reports from their web pages and going forward they are planning to provide API end points to give us the data required in the form of multiple pre-defined reports. But, I am just wondering, if there is any other secure and feasible method with which we can get the current state of their entire database filtered for our company, which gets automatically refreshes every few hours?

Thank you,

KP