Removing an old mailbox and post is usually the first step to replace the existing mailbox post with a brand-new unit. The task’s difficulty usually depends on how the previous installer secured the old post in the ground. If it was just buried in soil, it would make removal a whole lot easier. If the post was set in concrete the job would be considerably more difficult.
One option is to find a new location across the front of the yard staying within the USPS guidelines if that is a possibility. If so, you can simply cut off the existing post a little below ground level and cover it with soil.
If the previous post was set in the ground and backfilled with soil removal should be relatively easy. Dig around the post until with shovel and digging bar if available and once the unit is moving back and forth it should be able to lift out without too much effort. Having some assistance at this step would be helpful.
If the post was set in concrete, it will be a much more time intensive process. There are a number of methods that can be used, but the easiest would be to contact an experienced mailbox installer and have them remove for you. If this will be a DIY project, digging around the base until it can be lifted out is one way, another approach is to dig only on one side until the post can be moved in that direction and dragged out of the hole with a chain or with a suitable vehicle (pickup truck, etc.) and utilizing a jack system that many fence installers use is another method. With a post secured in concrete to a 24” depth this will be the most difficult and time-consuming part of the job.