Working with external parties

My question is how you can adopt an agile mindset when you are dependent on external parties who work to their own sprints, or deliver in waterfall?

Why not promote transparency and awareness of such impediments to integration, frequent release, and the establishment of empirical process control? Wouldn’t that be adopting an agile mindset?

My question would be, what do you hope or expect will happen as a result?

As @Ian pointed out the key to an "agile mindset" is transparency of information.  Based on that transparency the organization will inspect and adapt accordingly using empiricism as the basis of those decisions.

Agile is not a noun.  It is an adjective meaning "marked by an ability to think quickly; mentally acute or aware" according to dictionary.com.  How do you think that your company could satisfy that definition while depending on the resources you mentioned?  If you can do so while incorporating empirical practices you are being an agile organization.

While I certainly agree with the advice given by my predecessors, it's worth noting that because you don't control those third parties, the most critical part would be to get them onboard. Their buy-in absent = you can't do much.

Existing contracts may need to be amended, for you can't have a commercial relationship otherwise.

Always keep in mind these values, and see how your own organization is feeling about it. How are the vendors feeling?

Individuals and interactions over processes and tools

Working software over comprehensive documentation

Customer collaboration over contract negotiation

Responding to change over following a plan

You've got a lot of discovery ahead of you.