From docs:
To configure the chaincode collections on the channel, specify the flag --collections-config along with the name of the collections JSON file,
Is it possible to update private data collection policy after instantiation of the channel? In my case I want to add a member or remove a member from policy for a particular private data collection.
Or if there is another approach, I would like hear it too.
Yes you can do that, there is a peer chain code upgrade command that can be used after instantiation.
Refer: peer chaincode upgrade
where you can specify --collections-config flag with your new collections-config file by either adding or removing member from a policy.
Your second question on another approach, If you want to add/remove members you can consider creating a new channel but that depends on your usecase. For this you can refer to
When to use a collection within a channel vs. a separate channel
