Possible Clues:

• National Celery Month
• With 2 Down, tea party member of literature
• When Daylight Saving Time starts
• Surname of the Alcott characters at the starred answers' starts, or 2020 month in which women made all the Universal Crosswords
• Refuse hard slog
• “Beware the Ides of ___”
• Nowruz month
• Month for walking?
• Demonstration of the month
• Start of spring walk