The phrase "a responsibility that has" is correct and usable in written English.
You can use it when discussing an obligation or duty that exists or is currently relevant.
Example: "As a team leader, I have a responsibility that has a significant impact on the success of our project."
Alternatives: "an obligation that has" or "a duty that has".
It is a responsibility that has apparently weighed on him.
With situations such as the high-profile technology breakdown suffered by NatWest earlier this year, jobs like Anthony's carry a responsibility that has both advantages and disadvantages.
What makes Robertson so tough is his ability to retire left-handed batters, a responsibility that has assumed greater importance because of injuries to Rafael Soriano, Joba Chamberlain and Pedro Feliciano, and the inconsistency of Boone Logan.
Like the attorneys-general, these cases suffer from the weakness that the insurers can, in theory, claim money only if the tobacco firms are liable for smokers' illnesses (a responsibility that has rarely been established).
It's more than a job; it's a responsibility that has to be carried out.
He'll be Digg's first head of product, a responsibility that has been shared at various times by founder Kevin Rose, CEO Jay Adelson and Chief Strategy Officer Mike Maser.
"I think the Senate and the Congress as whole has an oversight responsibility that has to be carried out here anyway.
At 16, Gailan has had to mature quickly – a sense of responsibility that has combined with a fractured childhood and missed opportunities to ferment into a potent depression seething just under the surface.
It has given so many students a degree of independence and a sense of responsibility that has been missing from so many sixth form establishments.
The Constitution, adopted after one of the military's coups in 1980, assigns the army to intervene in politics to defend of the republic, a vaguely defined responsibility that has until now been read as granting the military unconditional immunity.
By contrast, the Gingrich Republicans became obsessed with balancing the budget, a strategy of "fiscal responsibility" that has proven a consistent political loser since the New Deal.
