Assuming you can trust the format, it would be easiest to just split on /
and check that the year falls in this range.
var year = date.split("/").pop();
valid = year >= 1600 && year <= 9999
If you have to use a regex:
/\d\d\/\d\d\/(1[6-9]\d\d|[2-9]\d\d\d)/
may be what you are after.
If you need more sophisticated date parsing, you should use something like moment.js
var year = moment(date, "DD/MM/YYYY").year();