How to unzip tar.Z file through CHEF cookbooks

There's actually nothing built into Chef for doing extracting a tar file. You have two options, either you can use the execute resource to shell out and untar or use some community cookbook like the tar cookbook that have custom resources defined for extracting tars.

In the execute resource example it might look something like

execute 'extract_some_tar' do
  command 'tar xzvf somefile.tar.gz'
  cwd '/directory/of/tar/here'
  not_if { File.exists?("/file/contained/in/tar/here") }
end

Whereas the third party tar cookbook definitely reads nicer

tar_package 'http://pgfoundry.org/frs/download.php/1446/pgpool-3.4.1.tar.gz' do
  prefix '/usr/local'
  creates '/usr/local/bin/pgpool'
end

Since Chef Client 15.0 there is a archive_file resource built-in. It supports tar, gzip, bzip, and zip.

archive_file 'Precompiled.zip' do
  path '/tmp/Precompiled.zip'
  destination '/srv/files'
end