Can a plummer fix this air gap thing for the dishwasher and what would it cost?

I take it that you have a counter top air gap. We've had nothing but complaints on them. You don't need a plumber, you just need to purchase a longer discharge hose and install a high loop air gap. ( we have never had a complaint on a high loop air gap.
Take a look at the image I've put up. Run the hose up next to the counter top and secure it with a pipe strap. Now connect to the drain through the disposal (Note: there is a knock out plug that you ill have to remove) or if you don't have a disposal swap the drain tailpiece for a branch tailpiece (see 8image) . Take the counter top air gap out and replace it with a soap dispenser or a Insta-Hot unit. Your choice. You can not forget about a air gap malfunction. You're set for life. Good luck, Tom

... however, if your Code requires that you have to have an Air Gap, than have it removed, remove 7/8" gravity discharge hose too , clean them both and reinstall. If you want to purchase new one, you can do that too. Air gaps are under $10.00. Should take 30 minutes to do so plumber should charge you his "service call" charge + parts. Hope that helps. Milo

Code or not. I advise what will work the best and even though we have had countless complaints about faulty counter top air gaps we have never had, even the first complaint, on as high loop air gap plus my company has installed high loops in all our condo and single family homes with no complaints. I say go with what works! Good luck, Tom