The most common and most likely answer to this crossword clue is the 9 plus 5 letter word DIFFICULT TIMES
I've seen this crossword clue in Independent
D
I
F
F
I
C
U
L
T
T
I
M
E
S
Buddy explains!
The straight part
We know that "period of austerity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case period of austerity = difficult times.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.