The phrase "an establishment to" is correct and usable in written English.
It can be used when referring to a place or organization that serves a specific purpose or function.
Example: "The city plans to open an establishment to promote local artists and their work."
Alternatives: "a venue for" or "a facility to".
When choosing an establishment to eat you don't often consider how well it will hold up in a zombie outbreak.
The trouble is that it is mighty tough to move from being inside an establishment to shaking it up.
His youngest brother, Sir Peter (1799 1861), founded in Leeds an establishment to make textile machinery and machine tools and was knighted in 1858.
Farage later attempted to clarify his comments, hitting out at "media fabrication" about his remarks, saying he had never said breastfeeding women should sit in a corner, but it was reasonable for an establishment to ask them to do that.
When a customer has a legitimate complaint, it is common practice for an establishment to apologize by way of free items or discounts, typically on top of replacing the offending item.
Also, do you feel that it's polite to ask an establishment to alter a dish to make it vegetarian or vegan (usually just asking them to keep the cheese off or telling them to sub the meat for extra veggies)?
Or was he the victim of a plot fabricated by an English Establishment to remove a Gaelic-speaking upstart who got above himself?
For example, tailoring a perfect species mix for a specific site in order to gain a quick establishment to prevent a weed population taking hold.
Jeremy Thorpe's life, for example, reminds us of both the potency of anti-gay prejudice and the willingness of a deferential establishment to turn a blind eye.
If someone goes into a retail establishment to purchase a satellite receiver, they are doing so because they want one, not because the car came with it.
At present, the Centre is a unique establishment to provide early detection and intervention services.
