Duplicate your original comp and open the duplicate in the timeline. Go to the point in your timeline where you want this new comp to begin. Hit the "B" key. This sets the beginning of your work area. Go to where you want the end of this new comp to be and hit the "N" key. This sets the end of your work area. (You may already know this, but I'm saying it just in case)
Now, up in the bar on top click "Composition", then choose "Trim Comp To Work Area". That should do it. I think you can also right click in the timeline comp and select it that way also.
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in the projekt window, select the comp, CMD+D to dublicate it, oben it, delete all the stuff you don´t need, set timeline duration as needed, then klick on COMPOSITION in the menu, set comp to workarea.