As mentioned, we can spread dragonflies, a beneficial insect that eats many mosquitoes a day both in larval form and in the air.
Dragonflies are also an important prey item for birds and bats, both of which have decreased in numbers in recent years and would benefit from more food sources.
We can restore some of our wetlands, where dragonflies breed, and try to eliminate standing water in urban areas as much as possible -- old tires, ditches, etc. Mosquitoes love wetlands too, but in a properly balanced system, their populations would be controlled by fish, dragonflies, and amphibians.
We should also continue research into gene drives and similar efforts to reproductively target a species for extinction.
At the same time, we should be careful not to damage the thousands of non-biting mosquitoes which are valuable pollinators. About 5000 known species exist of which only about 100 feed on blood, and about 9 of those blood sucking species carry deadly diseases. If we target just the blood sucking species while not affecting the others, the effects on the ecosystem should be minimal.
Mosquitoes are a remarkably effective and robust creature, dating back 100 million years, and existing in nearly every part of the world. They bring great misery to many species of animals and their extinction will not be mourned.