The most common and most likely answer to this crossword clue is the 4 plus 7 letter word CASE HISTORY
I've seen this crossword clue in The Times
C
A
S
E
H
I
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T
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R
Y
More clues leading to the result CASE HISTORY
Buddy explains!

The straight part
We know that "One doctor may look up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one doctor may look up = case history.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.