Gating a Turn on a Test Run, Not a Tool Call

You want a guardrail that operates at the level of "Claude thinks it's finished responding," not at the level of any individual tool call: before Claude is allowed to end its turn, the guardrail should run the test suite, and if it fails, block the turn from ending and feed the failure back so Claude keeps working instead of reporting done.

Which hook event is the right one to register this on?