I installed this 6x6 pressure treated post last year. The only load on it is a hammock. It has developed a large split. Should I use an exterior wood filler to fill it, or waterproof wood glue and clamp to close it up?
That's a "check" from the green wood drying out, and the very likely fact that the center of the tree is in your post.
It's structurally insignificant, utterly normal and expected, and you don't need to do anything about it. Trying to close it up will fail - it's a result of differential shrinkage (and is why wood you don't want to see such things in has to come from much larger trees, so the center of the tree is NOT in them.)
If you would rather not see it, cover the outside of the post with trim boards, or shingles.
You can make a cut from the surface to the pith (center of tree) when the wood is still green and un-cracked to define exactly where this inevitable shrinkage artifact will be, and make it tidier. That's about it.