If you purchase an annual pass over the phone or online, you do not receive the actual pass. You get a "will call" number or an exchange certificate. You bring the "will call" number or the certificate to an on-site guest relations booth to get the actual pass. The "will call" numbers and exchange certificates do not expire, so you can hold them as long as you like before you do the exchange. Even if the price of the AP goes up before you do the exchange, you will not owe any additional money. Your year of admission begins on the day you do the exchange.
Renewals are different. You have between 30 days before & 30 days after the AP expires to renew it for the renewal price. Your new year of admission begins on the date the original AP expires, no matter when you do the renewal. Depending on your plans, you may find it better to just let the old AP expire and buy a new AP that you can activate just before your next trip.