Formal:
* Implement: To put into effect.
* Execute: To carry out or put into action.
* Effect: To bring about or cause to happen.
* Enforce: To ensure compliance with.
* Authorize: To give permission or power to.
Informal:
* Put into practice: To make something happen.
* Carry out: To perform or complete.
* Do: To perform an action.
* Make happen: To cause something to occur.
For specific contexts:
* Pass (a law): When referring to legislation.
* Stage (a play): When referring to performance.
The best substitute will depend on the specific situation and the meaning you want to convey.