Very very rarely.
One big problem of inventing new characters nowadays is you cannot type it easily. Different from new English words, which a just new combinations of letters. For a new Chinese character to be shown or typed, it must be in some Unicode library. If it cannot be typed or shown, it won’t be very popular. If it cannot achieve certain popularity, it won’t be adopted into Unicode.
Yet, there are several scenario where new characters are invented and adopted officially. One I can think of is when new elements are invented. Chinese people are super keen on keeping all the element names single characters and obey certain rules(explain latter)
On the top are the new names for element number 113, 115, 117 and 118. The 113 and 115 names are not newly invented, but are rarely used characters(never used once in my life). But the later two are newly invented.
A interesting fact is that all the element names are carefully designed in Chinese, other than using direct translations. Here is a periodic table in Chinese:
If you know chemistry well and look carefully, you will find some rules laying behind it.
All gas elements contain 气, which means gas on the top. All metals except Mercury contains 钅at sides. This just means metal. Mercury contains 水, which means water as it is the only liquid element at room temp. All non-metals contains 石, as it means stone.
A pretty neat system right?