If I can get at the connector I prefer to de-tarnish it with Flitz, then after a bath in contact cleaner I’ll goop it up with dielectric grease, which ensures I will not have to do it again any time soon.
You can realign the leaf contacts carefully with a dental pick or, if that doesn’t come to hand, a pin with a short 90 degree bend in it. You can also truly realign the pins in specific connectors if the fancy strikes you; my front loader NES will now happily (and easily!) play cartridges without having to push them down.