Thanks for the reply Dave what you said sounds good. That was what I was thinking but wanted to ask around to make sure.

Thanks Kurt

I have someone that has built an arbor some years ago and treated it with Thompson’s water sealer and now would like the arbor painted white. I have pleasure washed the arbor and most of the wood seems to be in decent shape. My question is does anyone have any ideas as to best proceed in painting it?

Kurt, I'm not sure what "pleasure washed" is but it sounds interesting.

Any idea what kind of wood it is? Is really open-pored?

I think I would start with a primer of Kilz since that'll go on thick over almost anything. If the wood is quite dried out it'll probably take a fair amount of primer especially on any end grain surfaces. Then use an enamel based paint for the top coat(s).