This is something a lot of teams run into, at least the ones I've worked with and hear about from colleagues. And, as you might expect, there's room for a lot of tension between the two parties that use different methodologies for delivery. The fact is, if this is something that is simply necessary (there may be reasons), both teams will have to understand the trade offs of compromise. It really revolves around two concepts: change and planning. Conventional wisdom will say the agile team is more comfortable with change while the other team is more comfortable with a set plan. Both can be valid throughout the life cycle of a solution, but it's vital to understand which is best for satisfying the intended customer at any given time.
To answer your question about continuing to be agile in the midst of working with a more traditional waterfall team, I've found being abundantly transparent is vital to help spur collaboration and interactions. Transparency breeds discussion, which is a good thing so long as everyone understands the goal for why you're building what you're building. This is often times different from personal and professional motivations.
Do we know enough about how this will impact our customer to plan out x, y, and z 6 months in advance? Waterfall and agile can co-exist here.
Do we need more information about how this will impact our customer before fully delivering a big bang feature? It's probably better to compromise on a plan to deliver on incremental, iterative experimentation.
It's a tricky situation, but at the end of the day collaboration and the willingness to choose the best approach based on customer impact usually helps mitigate a lot of the issues such a situation can present. Snags and hiccups will happen; no one methodology will win. But life becomes easier when everyone is aligned on being transparent, the trade offs of making a decision, and ultimately doing what's best for the customer.
