Contingency matters don't exist in Centerbase as a separate fee arrangement setting under Billing, but there are a couple of ways to simulate a contingency matter.
The Fee Arrangement field exists within the matter details screen as a label to denote those matters that are to be Contingent matters.
One option is to go into the Matter, click on the cog > Billing settings, and set the Fee/Expense Bill Generation Settings dropdown under the Bill Generation Settings section to 'Include Only Expenses'. That will prevent Time Entries from getting on bills, and when you're ready to bill time, you can change it back.
The other option is to go into the Matter, click on the cog > Billing settings, and select Non-Billable under the Billing Entries section. That will hide all billing entries on bills until you're ready to bill. To change the entries back, you'll need to mass edit the entries from the Billing Entries tab on the Matter. (Mass Updating Records – Centerbase)