The most common and most likely answer to this crossword clue is the 5 plus 8 letter word BLOOD PRESSURE
I've seen this crossword clue in Financial Times
B
L
O
O
D
P
R
E
S
S
U
R
E
More clues leading to the result BLOOD PRESSURE
Buddy explains!
The straight part
We know that "a doctor might observe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a doctor might observe = blood pressure.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.