Personally, I don't see much of a problem. My retorical question would be, "What's the 'problem'?" But don't answer it because I don't think it matters.
If the fence post has concrete all around it, then you need to 'bust' the post out. A neat and clean way to do this is is to cut the concrete out with a saw specifically made to cut concrete. You can rent one. You need to find out how thick the concrete is so you get the right blade diameter. Then if the post you're removing is 4x4, I'd cut out an 18" x 18" area (in total), and take out the post. Then I'd put the new post in and seal it back up with concrete.
A couple of points ... You didn't say if you're using PT wood, vinyl, or an exterior pine, or whatever. Depending on what you use, find out what you should do to prep the postd FIRST before you submerge it in concrete. (I won't elaborate on the prep because I'm not in the lots-of-writing-mood today. Sorry.) DO this BEFORE you cut the old post out. Also, put in a 4" bed of gravel below the frost line, and work up from there. To prevent upheavel from freezing and thawing, your concrete should 'start' below the frost line too. SO, if the 'line' is @ 18", dig down to at least 24". I also drove a couple of galvanized nails into the post on the sides down towards the bottom and top (but below the base of the driveway) for 'stability'. I've heard stories where folks didn't do such a good mixing job that the post pulled right up! I left the nails stick out of the post far enough that it couldn't be pulled up.