My first thought was to use one of those post bases but I don't think
it would be sufficient to withstand the horizontal loads placed on it
by the fence's gate. It would only be attached to about 4" of the
post at the base.


"J" wrote:
Clean out the old hole.
Coat the inside with concrete bonder (basically watery glue - but you can
get it at the HW store)
Get a piece of 1/4" x 3-1/2" x 24-30" steel plate with 1/2" holes bored in
it.
Set one end of the plate in the hole and grout it in place with the plate
perpendicular to the plane of the fence.
Cut a 1/4" wide slot in the post.
Drill holes to match the holes in the plate.
Use some 3/8" bolts and washers to secure the post to the plate.
One of the ready-made post bases may work too, but may not fit in the hole
you have.

It will make replacement easy in the future.