"existing responsibilities" is correct and usable in written English.
You can use it when referring to present obligations. For example, "He was unable to take on any new tasks as he was already overwhelmed by his existing responsibilities."
The Council's existing responsibilities were also broadened as a way to have a more representative government.
In addition to her existing responsibilities, she was given two new groups to manage.
But I have rarely been able to act on it, as I have been overloaded with existing responsibilities.
Calculate how much work employees will have to do beyond their existing responsibilities to implement the change.
This structure was proposed by the SEC because the SROs have existing responsibilities to oversee the securities markets.
The Medicare agency, which can barely perform all its existing responsibilities, will face immense challenges in getting the new program started by January.
But as with strategy planning, internal communication is sometimes another unit's existing responsibility.
The Paris agreement actually weakens the existing responsibility of rich countries to provide finance to poorer countries to help them adapt.
5 There is no legal responsibility for rich countries to help poorer ones with adapting to climate change The Paris agreement actually weakens the existing responsibility of rich countries to provide finance to poorer countries to help them adapt.
In 2007 he assumed responsibility for some local lines, which now form the London Overground network, adding to the existing responsibility for the London Underground, trams and buses.
Unlike the EU proposals, however, Mr Obama's plan also makes the Fed directly responsible for the supervision of all firms deemed too big to fail in addition to its existing responsibility for bank holding companies and some banks.
