There is no deadline to file an over 65 exemption. You will be granted a percentage of exemption depending on how many days in the year you qualified for the exemption. The percentage of the exemption is calculated by taking the number of days in the year you qualified and dividing it by 365 days.
Example: You file for an over 65 exemption on a property and claim October 1st, 2017 as the date you qualify.
In 2017, October 1st was the 274th day of year. This calculates to 75.07% of year, meaning you would have qualified for the over 65 exemption for, 24.93% of the year. If the over 65 exemption is $50,000, you would be granted an exemption amount of $12,465 (24.93% * $50,000) for 2017. In 2018 you would start getting the full $50,000.
Here is a helpful link (Click Here) to help you calculate the correct number of days in the year (be sure and selected the correct year, it is defaulted to 2017).