Like Ross is suggesting by asking you to provide your real command is that all depends on how you are pushing your info to said file.
I for example often use an app called tee with the option -a for append, but if you're just piping stdout to a file with >, then a simple >> would suffice to append. But, as you indicated, you wanted a date to tell you were new info is added. I know that's possible, but it's a bit trickier.
Just creating a dated file is a lot easier.
Here's an example where I regularly change settings of all groups.
/home/user/gamadv-x/gam print groups | /home/user/gamadv-x/gam csv - update group ~Email showInGroupDirectory true who_can_join invited_can_join who_can_view_membership all_in_domain_can_view who_can_view_group all_members_can_view who_can_leave_group none_can_leave include_in_global_address_list true | /usr/bin/tee -a /home/user/gam-activities/Fix.new.groups-$(date +'%F').txt
It's of course only the bit on the end that's relevant.
-$(date +'%F').txt
That will grab the current date from the shell and insert that as part of the filename at the end. You can format the date as you please. See man date for the syntax.