The wall outlet is the older 3-prong 220V, the dryer came with the modern 4-prong 220V plug. Is there a simple 3-prong male to 4-prong female converter that I can buy on the market?

You can replace the 4 prong with a 3 prong dryer cord. It's cheaper than an adapter or rewire. Follow the instruction with the cordset and you will put the ground strap on the neutral.