Does high tensile steel rust

In Short. Yes.

Broadly speaking, any ferrous material (containing iron-Fe) will oxidise to create an iron oxide layer (rust)

In the construction industry this is normally protected against by utilising paint systems and in marine applications by utilising cathodic protection.

Alloys such as stainless steel (which does contain Iron) can reduce corrosion to very low levels. In the case of stainless steel, the alloying metals (such as chromium) react with oxygen and water to produced a thin protective oxide film which may be only a few atoms thick and will give the material a seemingly non corroded appearance.