The most common and most likely answer to this crossword clue is the 7 letter word COMPLEX
I've seen this crossword clue in The Guardian
C
O
M
P
L
E
X
More clues leading to the result COMPLEX
Buddy explains!

The straight part
We know that "Very involved/psychological state" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very involved/psychological state = complex.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does COMPLEX mean?
COMPLEX noun- A network of interconnected systems.
- A collection of buildings with a common purpose, such as a university or military base.
- An assemblage of related things; a collection.
- An abnormal mental condition caused by repressed emotions.
- (by extension) A vehement, often excessive psychological dislike or fear of a particular thing.
- A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules.
- A complex number.
- To form a complex with another substance
- To complicate.
- Made up of multiple parts; composite; not simple.
- Not simple, easy, or straightforward; complicated.
- (of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- (of a function) Whose range is a subset of the complex numbers.
- Whose coefficients are complex numbers; defined over the field of complex numbers.
- A curve, polygon or other figure that crosses or intersects itself.