Hi @Romila baretto ,
Whether this issue happens to all users in this AD security group?
1.Please make sure this AD group is security group, because you are not able to add distribution groups to SharePoint groups.
2.Please check whether these users have permissions or not.
Settings > Site settings > Site permissions > Check Permissions

3.These users could try to sign out and sign in again to have their security token updated with the new groups.
4.And you could try to add this AD group to SharePoint site directly as a workaround.
Settings > Site settings > Site permissions > Grant Permissions > Show options > Select "Read" permission level

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