Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
There are some notes on the common reporting standard here and here.
Provided you disclose all your taxable income and gains, you really won't notice any difference in how HMRC deals with your taxes. The CRS is an agreement signed by 101 countries whereby the tax authorities in each country will provide one another with information relevant to taxpayers living in their countries as provided to those tax authorities by institutions in those countries. UK pension payers already inform HMRC about your UK pensions and the banks provide them with details of interest paid on accounts in your name. All that is happening is that non-UK institutions will tell HMRC via their local tax authority of income and gains made by tax residents of the UK from non-UK assets, investments, pensions etc so that HMRC can ensure that UK taxpayers with taxable non-UK income are disclosing it.
I hope this helps but let me know if you have any further questions.