The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 plus 2 letter word GRIN AND BEAR IT
I've seen this crossword clue in Financial Times
G
R
I
N
A
N
D
B
E
A
R
I
T
More clues leading to the result GRIN AND BEAR IT
Buddy explains!
The straight part
We know that "How stoically to suffer the intrusive paparazzi?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case how stoically to suffer the intrusive paparazzi? = grin and bear it.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.