Facebook for Business makes it easy for Agencies to manage clients FB pages.
Here is simple step by step walkthrough to request 'access' to your clients FB Page.
1) Once logged in to FB Business Settings > Pages: People and Assets Tab
2) Add New Page >> Request Access to a Page
3) Search for FB Page
4) Request the permissions you need
5) Once approved by page owner, you will find the page in your Facebook Business Pages section.
Now, you can assign your team members in the agency to work on the new clients page.