busy doing something; involved with somebody/something in an active and interested way

I can't come to dinner on Tuesday—I'm otherwise engaged.

They were engaged in conversation.

to be engaged in dialogue/discussion/debate

They are engaged in talks with the Irish government.

She is actively engaged on several projects.

We need to become more engaged with our history as a nation.

Mrs Scott is engaged with a customer at the moment.

I couldn't get through—the line's engaged.

I phoned earlier but you were engaged .

the engaged tone/signal

LEARNit Dictionary