There are different licenses that could apply here.
If the item is purchased from VideoHive, there’s a multi-use clause in the Standard license that would cover use in a series:
To be considered a series, all things in the series (eg episode, edition) must be connected, and be released within 1 year of the first installment. There is also a maximum of 52 episodes or editions within the series
For your example, if you use the logo at the start of videos released on your YouTube channel, your VideoHive license would cover you for up to 52 episodes within the next 12 months. If you want to use it in the following year, you’d need to buy another license for that item.
If the item came from Elements, there’s no equivalent to VideoHive’s “permitted multi-use” clause. For each new video, you’d need to add a license (using the button shown below, which you should see in your subscription downloads page). That ensures that the item creator is properly credited for each use of their item.
It doesn’t look like that specific item is available in Elements at the moment - there’s a list of all the current Video Intro items here: https://elements.envato.com/video-templates/titles