There is no built in place to do such.This is a ticket system, not a billing and time tracking system. That being said you could use internal notes, or add a custom field to the ticket details form for tracking. There are a number of threads and mods on the forums discussing this sort of thing.

Understand it's not in the system. It would be great if OSTicket adds this feature to the main build as it's needed. Other commercial solutions support this. It would also be good to add logic to SLA's for each customer that has an associated "max # of hours allowed" notion. Thanks OSticket team for the great work you have been doing!