Appending To Pagination Links
You may add to the query string of pagination links using the appends method. For example, to append &sort=votes to each pagination link, you should make the following call to appends:
{!! $users->appends(['sort' => 'votes'])->render() !!}
If you wish to append a "hash fragment" to the paginator's URLs, you may use the fragment method. For example, to append #foo to the end of each pagination link, make the following call to the fragment method:
{!! $users->fragment('foo')->render() !!}
Laravel 5.1 Pagination: Displaying Results In A view Documentation
In your case it will be something like this:
{!! $users->appends(['search' => $searchTerm])->render() !!}
Also, you can check the lesson Crazy Simple Pagination, it's in Laravel 4 but the idea is the same.