When a person is trying to get from one place to another with someone driving between those two points, we say he's trying to find a "ride".
For example you can say "I'm looking for a ride to New York". Or "I got a ride to New York". A driver can say "I gave him a ride".
But what is a "ride" from the driver's perspective? If a driver is looking for a passenger, you can't say "he is looking for a ride" since that implies he has no car to drive.
Is there a noun to describe the activity from the driver's perspective?