How to fix a crack in the corner of an outside wooden lamp post
You'll have to do a little checking to determine if you can clamp that seam back together. It might have been a poor fit to begin with in which case you won't be able to clamp it back. Try getting a hold of a clamp similar to the one pictured below and see if you can close the gap. If you can, get some good exterior wood glue and have at it. If you can't close the gap, get some quality wood filler that's paintable and fill the gap. Then paint. A quick and easy fix would be to just caulk it but it looks like a nice light so do it right.
Picture from amazon.com