Yes. Your new membership year will only start when your current one expires so you will not lose any days.
Please note that If you change from standard to concessionary membership this will not happen automatically as you have to take out a new membership because our database does not hold your age. However, the change will be picked up by our database and we will amend the expiry date of your new concessionary membership so you do not lose any days. A confirmation email confirming this will be sent to you.