The most common and most likely answer to this crossword clue is the 4 letter word DEEM
I've seen this crossword clue in The Times
D
E
E
M
Buddy explains!

The straight part
We know that "Judge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case judge = deem.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 DEEM mean?
DEEM noun- An opinion, a judgment, a surmise.
- To judge, to pass judgment on; to doom, to sentence.
- To adjudge, to decree.
- To dispense (justice); to administer (law).
- (ditransitive) To hold in belief or estimation; to adjudge as a conclusion; to regard as being; to evaluate according to one's beliefs; to account.
- To think, judge, or have or hold as an opinion; to decide or believe on consideration; to suppose.