Both Uses of

intervene
in
The House of Hades

"He means we've already tried," Hazel intervened, and the coach gave her a grateful look.†
p. 262.1

intervened = got involved or came between

Definitions:

(1) (intervene as in: intervened in the war)
the process of getting involved to influence an outcome
The exact meaning of intervention can depend upon its context. For example:
- "intervention program for at-risk youth" -- a process of trying to influence the direction of someone's life
- "medical intervention" -- action taken to improve a medical outcome
- "military intervention" -- interference by a government in affairs of another government (in this case to interfere militarily)
- "had a family intervention" -- an organized meeting of family members to encourage someone (who is often surprised) to recognize and work at solving a problem such as substance abuse
(2) (intervene as in: in the intervening years)
something between two other things -- especially the passage of time between two events
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Much more rarely, intervene can mean:
in various senses, including:
- to verbally interrupt -- as in "Not now!' she intervened."
- to be physically between -- as in: "You can't walk from one hill to the other because an impassable river intervenes."