Yes, you can keyframe the parenting of a layer in after effects to turn it on and off at specific times in your animation. Here’s how you can do it:
Select the layer you want to parent to another layer and drag it onto the other layer in the Timeline panel. This will make it the child layer.
Open the parent layer and find the point in time when you want the child layer to start following its movement. This could be at any point in the parent layer’s animation.
Create a keyframe for the child layer’s “Position” property at this point in time. This will lock the child layer’s position to the parent layer’s position.
Move the playhead to the point in time where you want to turn off the parenting. You can do this by dragging the playhead in the Timeline panel or by scrubbing the current-time indicator in the Composition panel.
Select the child layer and open its “Parent” dropdown in the Timeline panel. Click the stopwatch icon next to the parent layer to create a keyframe for the parenting property.
Move the playhead to the point in time where you want the parenting to turn back on, and create another keyframe for the parenting property by clicking the stopwatch icon again.
Finally, adjust the parenting property keyframes to turn the parenting on and off as needed.
You can also use expressions or scripts to automate the parenting on/off process, but keyframing is the most straightforward way to achieve this effect.