"Rightward shift" refers to a movement or change towards the right side of something, often representing a shift towards more conservative or traditional beliefs, values, or policies. Full definition
The collapse of the 2009 cap - and - trade bill had more to do with the dramatic rightward shift of the Republican Party — away from its earlier centrist position on climate change — than with Obama's lack of effort to push it through. (ensia.com)
In a move which is likely to significantly increase the pressure on the prime minister, Ms Le Pen argued that the speech marked a significant rightward shift across Europe. (politics.co.uk)
But the entire Jewish community is experiencing a rightward shift these days. (religion-online.org)