Many ways to do this, including mathematically, but here is an opinionated approach based on experience.

From a colour theory perspective both the brand blue and green have similar values (saturation/luminosity). I don't think you need any more bright colours in the palette. You could pick either as the primary colour.

Use the primary colour for call to action buttons and links. Use it sparingly to highlight the primary functions of the page.

Create tints (lighter) and shades (darker) of your secondary colour by adding white and RGB black in 20% increments. This gives you a choice of colours of varying intensities for colour blocks and structural elements.

You also need a neutral colour in your palette. This is often grey or sand, but you can add a tiny amount of green or blue to make the grey less boring. This is commonly used as a background to help define focal areas of the page.

I know a lot of designers would find this approach quite dull, but it's failsafe, and quite similar to the one taken in Google's Material Design.