Of course you do! But the English rules don't actually say it. And I don't see an FAQ on the boards here. We infer it from the End of Round section on Page 7 where it states that:
"At the end of any non-payday month, the unhired cards on offer stay in place; place 1 Mon on each such card (this can happen twice with each card, so here can be a maximum of 2 Mon on any card)."
At the end of the PAYDAY section after Food Payment a fourth step should be added:
"Refresh Hiring Pool
Remove the ending season's Occupation cards in the hiring pool from the game, and add four from the new season's stack."
if this is the case, the rule under the heading PAYDAY should read at the end of its introductory sentence "there is a Payday that has 4 (not 3) steps.
You missed this paragraph in End of the Round:
"After each Payday, you must remove any leftover fish tokens and replace them with the tokens for the next season. Then, you must discard all occupation cards on offer (put any coins on them back into the bank) and replace them with 4 new occupations cards of the upcoming season."