now that; since; as long as~
Expresses that since a certain decision or situation has been made, one must follow through with the corresponding commitment or consequence.
This pattern is used when you acknowledge that a certain action or decision has been made, and therefore you have a strong obligation or expectation to follow through. It often appears in formal or written statements, speeches, or serious conversations. It conveys a sense of determination or resignation based on a premise.
The nuance is similar to 'now that' or 'since', but it carries a heavier sense of responsibility. For example, if you say 約束した上は, you mean 'now that I've promised, I must keep it, no matter what.' It is not used for casual, everyday situations like deciding what to eat for lunch.
Note that 上は is quite formal and is often found in business or public announcements. In casual speech, you would more likely use からには, which has a similar meaning but is more common in spoken Japanese.