An application of Ironite would be a good start, IMHO. Easy to apply granule, but follow the label closely - too much can cause temporary phytotoxicity.
Another good source of iron would be Azomite, a ancient seabed mineral with many other micronutrients beside iron. Soil tests usually show a more or less, a deficiency in magnesium too, along with a iron deficit. Usually clay soils ( which are mostly commonplace in the SE U.S) have enough of the micro nutrients, but a very low p.H can lock up iron too. You might get your soil's p,H tested too.
Many times, in very acid soils, a timely application of dolomite lime will correct a chlorotic issue, and a magnesium deficiency too.