The phrase "arise further" is correct and usable in written English.
It can be used in contexts where you want to indicate that something is increasing or developing to a greater extent.
Example: "As the discussion progressed, several important issues began to arise further, requiring immediate attention."
Alternatives: "emerge more" or "develop further".
Potential problems could also arise further down the line.
It is now reorganising its scientists into multi-disciplinary teams to get them to talk to each other, and thus to take early account of problems that might arise further along the pipeline.
Not for them the "Westminster route" (first researcher, then ministerial bag-carrier, then candidate for a safe-seat) into politics.The circumstances in which the job of party leader would arise further bolster the prospects of these five MPs.
As new technologies emerge, new questions continually arise, further complicating matters.
Most of the accidents arise further to a relaxation of the surveillance and the awareness of the parents.
Under this definition, the replicator is causally responsible for all of the various effects that arise further down the biochemical or phenotypic pathway, irrespective of which entities might reap the long-term rewards.
Similar verification hurdles arose further down the chronological chain.
When the hypothesis of a link between vaccination and a possible adverse outcome arises, further investigation is required to confirm or refute the suspicion.
Some authors have modeled mutations arising further back in an invasion as well (Klopfstein et al. 2005; Travis et al. 2007; Hallatschek and Nelson 2008).
Players like Rubin represent a new breed of nimble power-broker Janine calls in her book Shadow Elite "flexians". Flexians move seamlessly back and forth among venues of influence when a new opportunity arises, furthering their own (not-fully-revealed) agendas and those of their associates.
Without orders and duties, a perceived lack of authority could arise and further disgruntle the employees.
