## presuming your sample vars for dir, old, new
## Somewhat untested, but . . .
use Path::Tiny qw( path );

my $iter = path( $dir )->iterator( { recurse => 1 } );

while( my $path = $iter->() ) {
  next unless $path->is_file and $path =~ m{\. $old $}x;

  my $new_path = $path->basename( $old ) . ".$new";

  unless( my $ret = $path->move( $new_path ) ) {
    warn "Problem moving '$path': $ret\n";
  }
}