If you pause an automation (by making it inactive using the toggle), contacts will also be paused at the step they are currently at. When you resume it (by making it active using the toggle), they will resume the automation where they were.
If the contact was in a “wait” or “wait until” action, the countdown will continue running.
For instance, if you paused it on day 29 of a 30 day wait, and then activated the automation seven days later, they will continue to the next step of the automation when you reactivate the automation. If you paused it on day 10 of a 30 day wait, and reactivated it seven days later, they’d wait 13 more days and then continue to the next step.
If you have a “wait until” condition that waits for 30 days OR a link click, and you pause it at day 29, and then reactivate it seven days later, the contact will be sent to the next step regardless of whether they clicked the link, because the wait timer has expired.