Project: Add ticket time to time spent

Hello,
perhaps a beginner question, but doing research on it, I couldn’t come up with a useful answer…

Is it possible to move/add a ticket to the Tasks header or add the time spent on a ticket to the Time spent overview? E.g., if a call comes in under a service contract and a ticket is opened and subsequently closed and falls under the service fee and is not invoiced, there seems to be no way to add the time spent on the ticket to either the Tasks or Time spent. Is that correct?

Thanks!