Is it possible to book a flight at the gate after deplaning from another flight?

That probably depends on the airport. In general, they're not equipped at the gate to sell you a ticket, but it might be possible.

If you got in early enough you could leave the secure area, go to the ticket desk, book a ticket (likely expensive) and then come back.

The simplest answer might be to try to buy a ticket online, if it will let you, as soon as you arrive at the airport. You can then check in online, or if not possible, go to the podium for the flight's gate, explain what you did and they can print you a boarding pass.

This, of course, assumes you have no checked bags.

You may or may not be able to buy at the gate and it's hard to predict whether you can or not. Your best bet would be to try buy one directly on the United App and you can also check in there. United is in terminal 7 and 8 at LAX. Most Santa Barbara flights leave from terminal 8. A 30 minute connection is doable, if you have no checked luggage and the incoming flight is on time, especially if it also gets in at Terminal 8.

United minimum check in time is 30 minutes for LAX. You must also be at the gate at least 15 minutes before departure. See https://www.united.com/web/en-US/content/travel/airport/process/default.aspx#minimum-reqd-times

EDIT: edited ticket availability at the gate.

(I've been working adjunct to the airline industry for 20 years--those check-in kiosks you see? That--along with some other team members, of course--was I, starting in 1996, with the first fully successful kiosks fielded for NorthWest Airlines in February of 1997.)

So, for this: the numbers won't work. In general, check-ins (never mind purchases) are limited to X minutes before the scheduled departure time. The usual minimum is 30 minutes before departure. You won't be able to get off the plane and over to the next counter in time--because the arrival and departure times are already separated by 30 minutes. Even if you get in early, deplaning and getting yourself to the next gate is going to eat that time pad. No matter the privileges assigned to the gate agent sine code, the GDS (reservation system) will likely reject the new reservation because of time constraints. Even if overridden and you somehow board the plane, your luggage will already be on the way to baggage pick-up when you board and won't be available in SBA when you land.

Can't you just rebook online now to add the LAX->SBA segment (assuming it's the same airline)? That saves you the time spent getting to the gate agent, getting the flight paid for, and so on--and your luggage ends up in the right place. Even if it's not the same airline--you could book now and save the extra effort.

Yes, Gate Agents can book new tickets (no cash though) but this wouldn't be my first plan because:

• They have a lot to do otherwise.
• You still have to comply with the 30-45 min purchase requirement and 2005-2035 is not enough time.

If you have cabin luggage only and the cost is not significant to you or whoever is paying, you can either:

• Book a cheap ticket and risk losing the change fee.
• Buy a refundable ticket likely at a higher price.
• Change your inbound to an earlier flight

My experience is yes. But you pay double or more for it. At the gate. If a seat is to be had. Not sure of America. Normally you are ahead upgrading seats at the gate.