The most common and most likely answer to this crossword clue is the 3 plus 4 letter word EBB TIDE
I've seen this crossword clue in The Guardian
E
B
B
T
I
D
E
Buddy explains!
The straight part
We know that "Recession in a seaside town" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case recession in a seaside town = ebb tide.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.