Animation Question

Hello,

I'm creating an animation for one of my objects but I'm having difficulty making it to the complexity I want. So I have the parent object, and lots of child objects underneath (where most need animation). However, I animate the main object first, but after I want to animate one of the child objects. However, upon doing this in the same animation clip, it takes the whole animation for the child object to get to the place it is (depending on where I ended the animation in the clip, but it starts moving from the start which is not what I want). I only want it to start moving in the clip section I start animating it in, not the entire clip. How could I fix this?

Cheers!