The phrase "constrain their ability" is a correct and usable phrase in written English.
You can use it when you want to indicate that something limits or restricts a person or group's ability to do something. For example, "The lack of resources available to the company constrained their ability to innovate."
Health-care organizations in the United States are also subject to additional regulations, which constrain their ability to do updates.
These companies thus have become vulnerable to economic slowdowns, which constrain their ability to pay for expansion and consolidation.
As he said on his Web site, he is keeping the multiple options to "further constrain their ability to engage in monopoly pricing".
He has advocated for stricter regulation of financial companies, including higher capital requirements for large financial institutions, which would constrain their ability to finance operations with borrowed money.
These delays constrain their ability to take full advantage of what is often their only opportunity for formal education and may limit their social functioning later in life.
These constrain their ability to make decisions about wage levels, education, health and social security policies, they dictate the privatisation of public services and utilities and open trade while maintaining the protective policies for crucial western agricultural and manufacturing sectors.
The troops are quoted as saying that the ousted general's strategy constrained their ability to fight the Taliban, and that they are losing the war.
That creates, in theory, the possibility that they will push for faster political changes, but it also constrains their ability to do so.
Most declined, citing a conflict of interest; clinical investigators had to sign confidentiality agreements that constrained their ability to talk about the progress of the trials.
