General synonyms:
* Hinder: To make it difficult for something to happen or to progress.
* Obstruct: To block or prevent movement or progress.
* Hamper: To make it difficult for someone to do something.
* Restrict: To limit or control something.
* Impair: To weaken or damage something.
* Curtail: To reduce something in extent or quantity.
* Delay: To postpone or slow down something.
* Thwart: To prevent someone from achieving something.
More specific synonyms:
* Stultify: To make something ineffective or useless.
* Frustrate: To prevent someone from achieving something they want.
* Disrupt: To interrupt or break up the normal course of something.
* Clog: To block something up.
* Constrain: To force someone to do something or to limit their freedom of action.
Phrases:
* Hold back: To prevent something from happening.
* Stand in the way of: To be an obstacle to something.
* Put a damper on: To discourage or lessen the enthusiasm for something.
The best word or phrase to use will depend on the specific context.