Q: Question on setting up a new drive...

I am looking to replace my current internal hard drive with something a little bigger, currently I have time machine synced with my current external backup hard drive. My question is can I use my same external backup hard drive to start "timemachine-ing" on my new drive without syncing it? In other words due to extra clutter I'd like to avoid reinstalling everything from my backup, so instead I'd still like access to all my old internal hard drive's stuff while still using the same backup external to timemachine my new internal hard drive.