"future responsibilities" is correct and commonly used in written English.
It refers to the tasks and duties that someone will be responsible for in the future. Example: "As an intern, I am eager to learn and prove myself, and I am also ready to take on any future responsibilities that may come my way."
– Deconstructing the zero-risk mindset: The lessons and future responsibilities for a post-Fukushima nuclear Japan.
Of course, bureaucracies respond better to past events than to future responsibilities.
Simply having one or more plans in place may ease the worry and uncertainty about future responsibilities.
One of FE's key future responsibilities will be helping to deliver the government's target of 3m apprenticeships by 2020.
Thus, the development of cultural competence among nursing students is critical in their preparation to assume their future responsibilities in the profession.
It is clear that, in beginning with his 18th birthday to prepare conscientiously for his future responsibilities, he tormented himself with thoughts of his inadequacy.
Now you can hide behind Super PACs that have no future responsibility to govern".
However, the second thread is a much more important one for the long-term future: responsibility.
Most important of all, isn't the result of such an initiative likely to be the complete abnegation by local papers of any future responsibility for courts and council coverage which, by implication, will justify yet further cuts in staffing?
But still I was surprised to see that Monday's Guardian editorial had stripped me of future responsibility for what the more reactionary parts of the human rights lobby have nicknamed my "secret courts" bill.
Understand your future responsibility from the horse's mouth (hiring manager) and your other team members.
