you might not be able to do since you are only replacing a section of an existing fence.
When you dig out that old post and loosen the soil and make the hole bigger, you have to use that much more concrete to find good stable hard walls. With your digging around and prying, you will not have cylindral type holes. So, the existing holes will work but with much more concrete than any clean post hole dug hole.
When I do this sort of repair, and when I am not using prefab fencing, then I will dig the new hole either two foot on either side of the old post hole. that way I have a fresh new hole and then I will have posts not equally spaced but they will be much stronger and easier to maintain. You could consider this also.
Now, if you mix the concrete stiff enough the post will sit OK over night on its own. Now too, if the fence is 6 foot high, you should go down at least two foot in the ground. I also like to crown the concrete up around the post to shed the water off and away from the hole. you need to be carefull about this crown because if its too high the fence pickets will not sit evenly with the others because of the crown.
Now, if you want you can build bracing for the post using two two by fours and two surveors stakes. Drive one stake at three oclock about four feet from the post, and the other at six oclock same distance. Get your two by four by 8 foot and screw it to the post and then to the stake and the same with the other. before the fastening make sure you level bubble.
Will set in 24 hours depending on the weather. use Fast set and dry in two hours.