Fixing leaky drain gasket
If you have a honer and it is not rusted through and through, you could clean up the outer lip, remove any calcium buildup, and ensure the outer lip of the sink itself is solid.

Also make sure it is not bent (the sink) and ideally, the drain tube is also perpendicular to the base of the sink. Make sure the sink is still sitting level on the counter top.

if everything is level, flush, and clean, you should be all set.

If the drain area of the sink is rusted through, you'll have to replace it, or epoxy it like mad. (then clean it, and seat everything).