"Set Layer Start Time" question

[Reindeer]

I understand that "Set Layer Start Time" will make a layer re-start from frame 0, on any given frame. But what I would need now is for the layer to start from where I am using the last pose, not the beginning.

Say my character has reached a certain pose on frame 1000. I want to create a new layer (duplicating the original one) that will start from there but not contain the clutter of all the previous animation.

What I'm imagining is a way to tell the duplicated layer "forget all animation from 0 to 999: the pose on frame 1000 is your new beginning, your NEW frame 0"

A relative frame 0 instead of an absolute one, if that makes sense...