"conditions which require" is correct and usable in written English.
You can use it when referring to conditions that need to be met in order to achieve a certain goal. For example: "The job offer included a signing bonus, but it was contingent on meeting certain conditions which require the successful completion of a probationary period."
Baquer Namazi has a serious heart and other conditions which require special medication, she said.
(I don't mean anorexia and bulimia, which are complex mental conditions which require specialist treatment).
"However," the doctors write, "this is frequently inappropriate as there are a multitude of medical conditions which require more urgent attention".
As for the working conditions, which require that Smith and Ayala stay backstage while the greatest players in the tennis world do battle on the other side of Armstrong Stadium's concrete walls?
Non-Hodgkin's lymphomas (NHL) are an extremely heterogeneous group of conditions which require important decisions to be taken at many points along the treatment pathway.
Meanwhile, existing in vitro data for cells exposed to mechanical stimuli are usually compared with those under static culture conditions, which require the careful design of control cases that are expected to subtract reasonably background noises from measured signals.
I'd already come up with a list of things that could be wrong – all were potentially sight threatening conditions which required urgent attention.
Knockout mice are so precious and expensive that they are kept in pathogen-free conditions, which requires them to be housed at vast expense in climate-controlled rooms and attended by every comfort known to animal husbandry.
Microbial populations exist in dynamic equilibrium with constantly changing conditions, which requires fast and fluid regulatory networks for optimizing cell functions.
Dependable complex systems often operate under variable and non-stationary conditions, which requires efficient and extensive monitoring and error detection solutions.
The fastest responses were obtained when a salient target was presented, while responses were slowest with target-absent conditions, which required extensive evaluation of the visual scene.
