An A record in DNS associates a name with an IPv4 address. This is no more magical than a simple database lookup (in a very real sense it is a database lookup), or looking up a name in an old-fashioned paper phone book and getting a phone number.
This means that when a user's web browser looks up which server it should contact for a particular site, it looks up a name and gets an IP address back. It then uses the IP address. There is nothing you can do on the server that has the IP address to change the lookup, because by the time the browser tries to contact your server all the DNS work is already done.
So, no, you cannot simply update A records on your server. Or, well, you can, of course, it just won't make a difference. Your client needs to change things on their end.
A common way to get the kind of intermediate step you want is to use a CNAME
record. Such a record tells the DNS resolver "Whatever you were looking for here, go look for it at this other name instead". Your client would then make their record be a CNAME
containing a name that you control, so that you can add, remove and change records for that name as you see fit.
The problem with this is that it's an all-or-nothing deal. A CNAME
redirects all other record types. So for a name that holds information for several types of services, you cannot redirect for only one. If you have example.org
holding IP address info, mail delivery info, DNS structural info and maybe Windows AD info, there is no way to only redirect the IP address info. It's all, or nothing.