Should I "wash" tea when re-steeping?

Ok, apparently my account got deleted so will try again:

When re-steeping your tea after a couple of hours, should you first “wash” the tea leaves and pour out the liquid or do you just pour new water on the cold leaves and re-infuse right away?

Normally I drink my tea with two to four hours in between and leave the leaves in my Gaiwan. But, the first infusion after a couple of hours is very strong and a bit colder than the following ones and if using Sheng/Raw there is a sourness to it.
How do you guys go about this?