Depending on the amount of damage, you might get away with just cleaning with vinegar or baking soda (use vinegar directly from the bottle, make up a solution of baking soda in water), try both on the dead battery or clip to see which works best. Use a Q-tip, scrub until there's no more crystalline stuff. Next use a cotton ball with baking soda solution to neutralize the vinegar, you want it to stop fizzing. Next use 99% isopropyl alcohol to pull out the water and dry the parts. Use copious amounts of alcohol, so that the thing is soaked, then blow all the alcohol out with compressed air. If alcohol got into any pots (potentiometers), they need to be relubricated with silicone oil spray.
If the damage to the battery clip (the wire and thing that clips onto the battery) is severe the clip needs to be replaced.
If the damage extends to the electronics, sometimes it needs to be repaired by unsoldering parts, cleaning up and repairing the circuit board and replacing the damaged parts. You can find countless videos of how to repair battery leakage on circuit boards.
You can take apart a 9V that hasn't leaked yet and make a clip from it that's better (much more robust) than the clips you can buy and have to pay money for.. Just take out the clip with pliers, solder wires onto it and glue it with hot glue.
https://youtube.com/watch?v=XlyTBnXjmsU
I've had to scroll through what's probably a hundred identical videos to find the oldest one from a White guy because electronics Youtube has been absolutely shitted and pajeeted on by brown retards, there's what seem like hundreds of videos and shorts of brown hands doing basic stuff with shitty filler music and spelling mistakes, why does youtube need a hundred identical videos of brown hands making 9v battery clips or some other similar shit. Imagine the amount of storage and bandwidth these subhumans are wasting, this is why we can't have nice things.