My left headlight will not work even after replacement. Why not?

Possibly a bad ground, if you have a meter, check the wires at the connection.

Sorry.....second part of answer, there is a relay involved and that could be bad....there should be a relay box somewhere under the hood. the relays are usually marked and all relays are the same, so find the headlight relay and switch it with another relay....if that fixes it go buy a replacement relay

I will give this a try. Thanks so much for your input.

I had this same thing happen with 2012 Chevy Malibu. The problem ended up being a connection to that light the GM shop called a pig tail. Changed that and no more problems. Hope this helps