I realise some time has passed since you posted your request, so you may have already found a solution.
Regardless, if you have access tocustom objectsin your HubSpot portal(s), you might be interested inStopWatch for HubSpot(a simple time tracking app designed to exist entirely within HubSpot). It allows you to track time against Tickets, Contacts, Companies and Deals using a "StopWatch" interface in the right sidebar on an individual record view, with the resulting "Time Logs" saved as custom object records within your HubSpot account. If you are interested, you can find the app's usage guidehere.
Hope you give it a try. Let me know if you have any questions🙂
The tools that exist will let you track things like "when the ticket was opened" to "when it was responded to" - but not things like how long your support agents spend looking after your customers. (Assuming that's what you're after.)
Tickets (in my opinion) are missing a "per activity" timer function. (A manual entry field would help!). I've implemented an "Accumulated time" manual property field for every ticket - but that has limitations if you want to report on all the time your agents spent on supporting customers in a particular time period.
The only option I have found so far is external app integrations like Toggl integrated with tools like Zapier - both applications are separately chargeable - so it gets expensive quickly.
There will be a time stamp associated with the ticket being created. If you would like a counter to be built in, I would recommend upvoting this idea on the ideas forum.