Sugestão.

Penso que poderia utilizar estes verbos nas frases que indicou na pergunta e é assim que interpreto, de acordo com o que pesquisei no âmbito dos seguros:

"...to be bound by the following terms." = "... estar sujeito aos termos seguintes:"

"... are not bound until underwriting review…" = "... só se tornam efetivos até à análise da subscrição…"

"... within 45 days of coverage being bound." = "... no prazo de 45 dias após a cobertura ser confirmada/após confirmação da cobertura."

The Definition of Binding

Binding is, by definition, the act of imposing a duty to keep a commitment. In the insurance industry, binding refers to insurance coverage, and means that coverage is in place, although a policy has yet to be issued.
https://smallbusiness.chron.com/binding-mean-insurance-31759...

If you meet with your Independent Insurance Agent to obtain an insurance policy, your agent may mention that your policy has been “bound”.
What exactly does that mean?
When your agent binds a policy, it means that he or she, as a representative of the insurance company, confirms that coverage is in place.
Your insurance coverage can be bound one of two ways: coverage can be bound through the insurance company issuing the policy or by the verbal or written commitment (called a “binder”) of an authorized representative of the company, such as an agent. A verbal or written binder is generally used to address the time period between the effective date of coverage and when the policy or endorsement is issued by the insurance company.
https://www.wnins.com/resources/personal/features/binding.sh...