Correct Clip Store is part of another license, usually partnered with another software called INcoder.
https://www.youtube.com/watch?v=0BA72S5MieY
While I recommend trimming your clips before importing you do have one more option inside the software. If you pull the material from the material manager thumbnail onto a scene director track you'll see it will create a green track. This is a reference to the frames of the video and you can simply grab the end of it like you would a layer in Ae and effectively hide the frames you don't want at the beginning or end of the clip. This needs to be done per clip.
You can also do some creative things with visual logic and scripting if you need it to be more dynamic than that.
#XPression