Can I keep my belt from a previous Taekwondo club I was a member of? 

This can be a tricky one, if your previous grade was from the TAGB, then the answer is generally yes as long as its not been too long since you last trained, however if its been a few years then you will need to do an official assessment and awarded a belt based on that. If your grade was with a Taekwondo club not part of the TAGB or a completely different martial art then unfortunately you will have to start at a white belt.