Yes you can apply for a scholarship after completion of your graduation. There are a couple of foundations in every country that grant scholarships. The foundation offers scholarship funds for undergraduate, master’s and PhD.
But it would be better to search for a suitable foundation before graduation. Check out the eligibility list of a scholarship and how to apply. There might be a minimum GPA rate to apply for a scholarship grant. Then study hard to achieve that score and also prepare necessary documents.
The papers might be all academic results, voluntary activities certificates etc. All these need time to arrange and apply for it. After graduation apply to any university or master’s or PhD. Being accepted by the institution one can apply for a scholarship.