The phrase "a further problem for" is correct and usable in written English.
It can be used when introducing an additional issue or challenge that affects a particular subject or situation.
Example: "The recent budget cuts present a further problem for the already struggling department."
Alternatives: "an additional challenge for" or "a subsequent issue for".
This report will now be referred to the Commons, and that could present a further problem for the Conservatives.
The report suggests the ADDE would go bankrupt without these funds, a further problem for the cash-strapped Eurosceptic group.
A further problem for such regulation is that utilities and similar industries normally operate in both competitive and monopoly markets.
A further problem for almost every country is the presence in most urban centres of storage or manufacturing facilities that contain toxic industrial chemicals and other toxic materials.
A further problem for Cameron could rear its head this week if the 18 Conservative MEPs join forces with a German eurosceptic party – Alternative für Deutschland (AfD) in the European parliament.
A further problem for spectroscopy is that in galaxies younger than 1 billion years, about 40% of the light comes from asymptotic giant branch (AGB) stars8, which are not well understood.
A further problem of current models for force-generation is, as pointed out above, that they assume an independent elastic element and require that the force-generating transition occurs in a large number of steps.
A further problem arises for the non-logical vocabulary.
The language gap is a further problem: Callela discusses, for example, how Mary Hunter's important monograph on opera buffa, standard reading on the subject in English-language scholarship, is rarely mentioned in recent German scholarship.
A further problem is that the assessment for eligibility for free nursing care has to be carried out by a registered nurse and, although dementia is often the main reason why someone enters a nursing home, few nurses have the relevant experience of dealing with people with these mental health problems.
A further problem was lack of access for humanitarian agencies because of the conflict.
