No, that's a closed shop, which has been illegal in the US since 1947. The usual arrangement in the US is a "union shop", where new non-union employees can be hired, but must join the union. In "right to work" states (mostly the ones that used to have slavery), union shops are prohibited.
> "union shop", where new non-union employees can be hired, but must join the union
This retains the problem that you have to join the union, and therefore are immediately subject to the union's negotiated rules on seniority, pay scale, benefits, etc. It's better than a closed shop, but doesn't solve the problem at hand here.
