This is a GREAT question that came up in our live writing session yesterday.
As a general rule, I would say DON'T use abbreviations in Writing Task 2.
For example, if you write 'Cognitive Behavioural Therapy' instead of 'CBT', you'll score highly for a number of reasons - precise and accurate choice of words, correct spelling, high-level vocabulary, risk-taking (it's so much easier to write 3 letters than 3 difficult words!).
If you want to refer to this word several times, it's ok to put CBT in brackets () the first time, so you don't need to write out the words each time (this is normal practice in academic writing).
You can see an example in this Guardian article about Ultra Processed Foods (UPFs).
Having said that, there are certain abbreviations that are so commonly used and well-known that it would be fine, even preferable, to keep the abbreviation.
For example, it would be more natural to write 'the BBC' than 'the British Broadcasting Company' (see more examples here).
In our Saturday session, Mina also asked if it's ok to use 'GP' (General Practitioner) as a synonym for doctor. I hadn't even noticed that she'd used GP in her essay - it seemed a very natural and acceptable abbreviation to use, as it's an everyday term, so it's fine to use it.
1. 'lazy' abbreviations like 'etc' 'e.g' and 'i.e.'
2. 'text message' abbreviations like 'DOB' (Date of Birth)