How to move views pager to different region as a block?
The easiest is probably the comment from @No SSsweat
Another easy option is to place the view in each region and hide the pager/content using CSS depending on region.
The javascript option may be possible depending if you have anything already in place, as you can move the DOM pager element programmatically.
The neater solution is to use some php code, the drupal way, probably someone has already done this for you, so look for a drupal contributed module related to view and pager or paging, and layout, those would probably be my keywords for a search.