Where a worker works through a Personal Service Company and contracts with clients via an agency, will the agency be made responsible for deducting PAYE and NICs if the Personal Service Company fails to deduct PAYE and NICs?

No. Provided the individual worker does not receive payments directly from the agency (other than salary which is assessed to PAYE) which represent payment for work done for clients the agency will not be considered to be an intermediary for the purposes of IR35.