there is a way in QGIS, using the TomBio plugin, to generate tetrad squares for an area of interest. More info and youtube tutorials available here.
To use this...
- zoom to an area of interest e.g. using a web basemap and the QuickMapServices plugin.
- turn on OTF projection and set to 27700 (OS GB)
- select "Tetrad (2km)", show grid squares
- click on the grid icon which doesn't have a yellow background
- Click and Drag on the canvas to select an area
this creates a memory layer but you can save it off as a shapefile etc. for later use.
The shapefiles that @charlesroper compiled on github - as mentioned in the comment - are really handy, but don't include tetrads (OS have LOTS of grids...)
I find grid generation can be slow if there are lots of cells so this may not be viable to generate the complete OS Tetrad grid, but hopefully it's useful for a specific survey/project