Hi Gene,
I looked a bit more and realized I have a better answer for you. The %(date) token can be used as a default value and automatically provides the current date. Ordinarily that's the full date, but if your Year field is formatted to only show the current year (field format 'y'), then only the current year will be displayed. See https://www.laserfiche.com/support/webhelp/laserfiche/10/en-us/administration/#../Subsystems/LFAdmin/Content/Custom_Date_Time_Field_Display.htm for more information on that.
One thing to note is that this requires a date field, not an integer field. Is there a reason you need this to be an integer field? If it's just that you only wanted to display the year and not the rest of the date, using the 'y' field format will address that as well.