Firstly there is no such thing as a frozen ATPL,only ATPL credits. It is a CPL /IR that you really want to keep current. In order to keep the aircraft rating current it will cost exactly the same as it would to keep a PPL current. The IR will cost a little more, you can let it go for a while, but don't exceed 5 years or you will have to resit the test with a CAA Examiner. If you let it go for more than 7 years and you will also lose the ATPL credits.
Be aware that if you are about to embark upon an ATPL theoretical course you have just 36 months from passing the last exam to applying for both the CPL and IR, you cannot afford to delay things.