The most common and most likely answer to this crossword clue is the 10 letter word YESTERDAYS
I've seen this crossword clue in Financial Times
Y
E
S
T
E
R
D
A
Y
S
Buddy explains!

The straight part
We know that "Recent past" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case recent past = yesterdays.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 YESTERDAYS mean?
YESTERDAYS noun- The day immediately before today; one day ago.
- The recent past, often disparaging.