open for business
1. Currently operational and accepting business from clients. We had a few setbacks with city regulators, but our new store is finally open for business!
2. To create and launch a business to do business with others. In this usage, a noun or pronoun is used between "open" and "for." My great-grandfather opened our first store for business 100 years ago today.
open for business
[of a shop, store, restaurant, etc.] operating and ready to do business. The store is now open for business and invites you to come in. The construction will be finished in March, and we will be open for business in April.