The verdict came from the Care Quality Commission's first inspection since the University Hospitals of North Midlands NHS Trust was created in November.
The hospital was at the centre of a Â£6m public inquiry into care failings.
But despite the CQC's overall finding being critical, the trust said it was "highly complimentary" about the standard of care in some areas.
Inspectors visited County Hospital, formerly Stafford Hospital, and Royal Stoke University Hospital, also run by the trust, in April. They carried out unannounced inspections in May.
Mid Staffordshire NHS Foundation Trust, which ran Stafford, was dissolved in November after a report concluded it was not "clinically or financially sustainable".
700,000
People served by the hospital trust
194,954
Combined A&E visits to the two hospitals (2013-14)
1,508 Beds provided across the two sites
8,848 Equivalent full-time staff employed by the trust
The NHS in Staffordshire was given almost Â£300m to create the new trust and relocate some services in the county.
The CQC said it recognised "that the leadership of the new trust has had the significant task of bringing together two organisations at a challenging time. We have seen that progress has been made but there is still more to be achieved".
The trust was rated as good overall for how caring its services were, but told it required improvement to ensure safe, effective and well-led services. It received an inadequate rating in relation to whether services were responsive.
Several initiatives within children and young people's services at Stoke were rated as outstanding in relation to whether they were caring.
Outstanding work was also seen in the specialised neurological unit at County Hospital, inspectors said.
But the trust was told it must address high waiting times in its emergency department, and inspectors noted the Royal Stoke had "consistently and frequently failed the four-hour waiting time target".
It also said the trust should review capacity and adequacy of critical care services, and communication between senior management and frontline staff.
Mark Hackett, trust chief executive, said: "Less than a year ago there were serious concerns about the sustainability, and therefore the safety, of services at County Hospital, but the CQC has now given the hospital 23 good ratings and just one inadequate rating."
He said the trust was addressing the areas for improvement the CQC identified.
A new NHS trust set up to run Stafford's hospital requires improvement, inspectors have said.