Late answer, but for anyone else looking for a fix to this: you don’t need to adjust your own theme’s CSS (there may be more than just the navigation that the TrustPilot widget overlaps):
For some reason TrustPilot’s widget has a default z-index of 1000. All you need to do is go into the TrustPilot app, click to manage Widgets, and select the widget you’re having an issue with. On the left-hand side will be a list of various options, and one of those will have a title like ‘Widget stacking order’ and a default value of 1000. Change this to 0 (which is the default value for z-index) and it should now appear just fine.