The phrase "already bound to" is correct and usable in written English.
It can be used to indicate a pre-existing obligation or commitment to something.
Example: "She felt she was already bound to fulfill her promise to help her friend."
Alternatives: "already obligated to" or "already committed to".
Mr. Trump's anti-immigrant rhetoric was already bound to reduce response rates among immigrants.
Unlike native New Yorkers, they were not already bound to the city by longtime jobs, families, schools or real estate.
Some financial planners advise against holding too many shares because so much of employees' financial well-being is already bound to the fate of their employer.
The reason for this is that the UK is already bound to very low tariffs on non-agriculture products by the World Trade Organisation.
Some observers say the fund's funding shortfall and bureaucratic malaise have dimmed expectations for the talks in Poland, which were already bound to be difficult.
A liquid containing viruses already bound to nanotubes would be injected into the bloodstream or abdominal cavity to seek out tumors.
It is already bound to shrink below 2% of GDP the level that NATO demands and which Mr Cameron endorsed passionately at the alliance's summit last year.
Built-in procedures (or just built-ins) are built-in to the interpreter and already bound to names when it is started (though it is still possible for you to rebind these names).
In his view, if an accident was long defined as chance, today only its timing and consequences are hard to predict; the accident itself is already bound to occur.
President Trump signed an executive order Thursday telling public universities like mine that we will lose our federal funding unless we do what we were already bound to do: Guard the First Amendment rights of our students, staff and faculty.
But the EU's emissions account for only 14% of the total, and its likely second commitment a 20% cut by 2020 would be no more than it is already bound to under European law.
