Yes, when you move you need to re-register to your new address. If you have registered since you moved to your new home, you do not need to register again. If you have not, you need register to vote again.
When you register to your new address, your new local authority will make sure you're removed from the register at your old address.
You can register online any time at gov.uk/register-to-vote.
If you change address, you will need to make a new application to vote by post or by proxy – your voting preference will not be carried forward to your new address.