How do you fix a fence gate so that it doesn't start shifting ?

You might need new hinges. but you might only need new screws. Get a galvanised fastener for the gate, it won't rust.

You could just make a new gate and buy new hardware and local hardware store. Check Pininterest for ideas on how to make a gate / door. I did this and it turned out fantastic...used cedar fence planks, 6ft...it was so easy

When gates start to sag, sometimes the hinges need to be replaced.Otherwise you could try some metal cable, like stainless steel and a turnbuckle which will help you raise the far bottom corner of the gate up. You'll attach the cable at the upper corner of the hinge end of the gate, with the turnbuckle in the center of the gate and attach the other end to the bottom corner of the non-hinge end. You can google search about turnbuckles online. We had a gate for our driveway, and every couple of years it needed a turn in the middle to tighten it up again which kept it from digging into the driveway and able to swing clearly... good luck!