Creating new polygon in between other polygons?

In QGIS you can achieve this just activating the Avoid Overlap option inside the Snapping Options.

Activate the Snapping and open the Snapping Options:

Here, select the option Advanced Configuration and click, to activate, the options Topological Editing.

Activate (check it) the layer(s) that delimitated the empty space and, finally, check the option Avoid Overlap in the layer(s).

Now you can just draw a new polygon with its nodes inside the surrounding polygons and the system it will avoid automatically any overlap creating a new geometry that covers only the empty space.

Addendum

Since the Version 3.14 QGIS has a new Snapping toolbar and the Overlapping option has a dedicate icon: