Managers at North Cumbria University Hospitals trust say they are facing some "immediate" problems with staff shortages at the West Cumberland Hospital.
Bosses have written to other trusts in the North East and North West of England to try to plug the gaps short-term.
The West Cumberland Hospital will lose its three remaining junior doctors in August which will make current staff shortages worse.
Gina Tiller has spoken after it was announce that she has been appointed as the new Chair of North Cumbria University Hospitals NHS Trust.
Gina Tiller has today been appointed as the new Chair of North Cumbria University Hospitals NHS Trust.
The announcement was made by NHS Trust Development Authority.
Ms Tiller has stood in as Interim Chair of the Trust since 1 February 2014. She is a former nurse, research officer and visiting lecturer at Northumbria University.
A Cumbrian NHS Trust has admitted liability for a mother's death in childbirth. But following a High Court ruling in London it will not have to compensate her son for his disabilities.
The North Cumbria Hospitals Trust admitted that the mother died from negligent care at the West Cumberland Hospital in 2002.
Her son, who's now 11, will need care for the rest of his life. But the judge concluded that his injury was not a result of negligence.
Hospitals in Cumbria are urging people to seek help and advice as early as possible if they feel unwell.
'The earlier, the better' campaign aims to alleviate pressure on NHS emergency departments this winter.
A new report by the Care Quality Commission has placed North Cumbria Health Trust in the bottom band of hospital trusts in the country.
The findings are based on data that includes death rates, serious errors and patient surveys.
13 risks were identified at the North Cumbria trust, including 10 that were elevated.
These included "never events" of incidents that should never happen in NHS hospitals, higher than expected death rates and issues over the time patients waited for treatment.
The report will act as a screening tool to identify which trusts need the most rapid CQC inspections and where inspectors need to focus their attention.
A stroke victim was sent home from a Cumbria hospital by a doctor because "no stroke unit was available", according to an NHS report.
The patient was discharged by a locum doctor from one of the hospitals run by North Cumbria University Hospitals NHS Trust, according to the trust's board papers.
An investigation has been launched by the trust's medical director into the process for appointing agency locum medical staff.
The locum in question no longer works at the trust, according to the document.
There were also three other "serious" patient incidents during June at the trust, which runs Cumberland Infirmary in Carlisle, the West Cumberland Hospital in Whitehaven and a midwifery-led service at Penrith Community Hospital.
One patient was operated on after mistakenly being given a local instead of a general anaesthetic.
Medics missed a "mass" which should have been spotted on a chest X-ray of another patient.
And a consultant coughed during a procedure which resulted in a patient moving - which they claimed "affected the clinical outcome".
The trust is one of 11 that was put put into "special measures" for "fundamental breaches of care" following a review into 14 trusts with higher than expected death rates.
The investigation, led by NHS medical director Professor Sir Bruce Keogh, found that none of the hospitals investigated was providing "consistently high-quality care to patients".
The North Cumbria Hospitals Trust has been placed into special measures by the Government.
It follows the publication of a report into high death rates at the area's two main hospitals.
Tim Backshall has been looking at the findings.
Only 35% of staff working at the hospitals in Carlisle and Whitehaven would recommend the treatment available there.
The NHS national survey of just over 100,000 staff members, found that of 161 NHS trusts in England, the North Cumbria University Hospitals Trust came bottom.
The Morecambe Bay Trust, which runs the hospitals in Kendal, Barrow and Lancaster also did badly, with only 49% of staff there recommending the treatment they offered.
In the survey, staff were asked to respond to the statement:
...and had to say whether they strongly agreed, agreed, disagreed, strongly disagreed or had no view.
The figures published in the Daily Telegraph found that nationally, around 60% of NHS staff would recommend the treatment at their hospitals to friends and family.