The phrase "to seek the injunction" means to ask a court or legal authority to order someone to stop doing something or to do something specific. Full definition
It held that these private plaintiffs have no standing under the state's civil rights law to seek an injunction on behalf of the public at large. (lawsitesblog.com)
The complaint seeks an injunction to halt the implementation of the board's new regulations that would allow state test scores to count for up to 40 percent of teacher evaluations. (huffingtonpost.com)
The owner of the copyright can take all the normal actions for copyright violation including seeking an injunction to stop the breach and / or suing for damages. (law.stackexchange.com)