The phrase "already constrained" is correct and usable in written English.
It can be used to describe a situation or condition that is limited or restricted at a prior point in time.
Example: "The project's budget is already constrained, making it difficult to allocate additional resources."
Alternatives: "previously limited" or "previously restricted".
Educators and institutions must identify appropriate e-learning tools for use in resource-constrained settings, analyze the effect of these modalities in decreasing the already constrained faculty time, understand the practicality and cost-effectiveness of e-learning use in resource constrained countries, and develop financial models for the sustainability of e-learning solutions.
Facebook is already constrained in Europe.
Low oil prices have already constrained exploration and production investment around the world.
Onerous security has already constrained what once was an excellent corps of political officers.
His behavior, already constrained by a series of societal norms, now has additional restrictions.
On the other hand, this illegal business entails a net loss for the already constrained budgets of these countries.
The feedback effects of such developments will only add to the stiff headwinds already constraining U.S. economic growth.
Big write-downs on these could erode capital, a shortage of which is already constraining lending and investment.
Business entities are compelled to fund generic advertising as part of a broader collective enterprise in which the regulatory scheme already constrains their freedom to act independently.
Concerns about the impact of income inequality are already constraining fiscal and monetary policy in developed and developing countries alike, as they attempt to extricate themselves from the hyper-stimulative policies adopted during the financial crisis.
Oakervee warned: "It is clear that all the main transport arteries both road and rail are rapidly becoming congested and are already constraining our ability to grow the economy to allow us to maintain our position in world trade and commerce.
