The most common and most likely answer to this crossword clue is the 4 plus 4 letter word ACID TEST
I've seen this crossword clue in The Daily Telegraph
A
C
I
D
T
E
S
T
More clues leading to the result ACID TEST
- Order dictates it's a critical assessment
- Crucial trial, one that may earn detective promotion?
- A police check that gives crucial result
- Searching appraisal makes one drunk cite DTs
- Police in rigged state trial that’s crucial
- Bill that is about Brexit finally gets critical appraisal
- Doctor dictates critical essay
- Process dictates rigorous appraisal
- Exacting examination – the paper’s marked in red
- Dictates new severe examination — involving litmus paper?
Buddy explains!

The straight part
We know that "searching examination" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case searching examination = acid test.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.