Is there a way to trigger a compositions start point in timeline based on the the end point of another layer ?

You could enable time-remapping and then subtract the out-point time from the actual time to shift around the playback, but well, that's essentially like trying to put out a fire with oil. In the end all those temporal expressions will slow down AE and prevent it from using e.g. MP-rendering plus you will have to figure it in every time you apply effects and other stuff. Far from an ideal workflow just to save two mouse clicks when otherwise you can easily drag around layers and snap them to markers, keyframes and other visible temporal demarcations just by holding down Shift...

Mylenium