First off, some professors will require you to include the access date for everything you cite. If yours is one of those, then yes, of course, follow those instructions.
MLA
Access date is optional and added after the url of a source. However, you should include it if the source itself doesn't have a date published or modified posted.
The date should follow the same DD Mon. YYYY rules as other dates.
Example:
“Transfer Student Application and Admissions." C.T. Bauer College of Business, University of Houston, https://www.bauer.uh.edu/undergraduate/future-students/transfer/requirements.php. Accessed 12 June 2023.
APA
Like MLA, it's a good idea to include an access date if your source doesn't post its published date. APA Style further adds: and if the page is likely to be updated periodically and there's not a page history archived.
Example: No date, possibly updated
How to report misinformation online. (n.d.). World Health Organization. Retrieved October 13, 2020, from https://www.who.int/campaigns/connecting-the-world-to-combat-coronavirus/how-to-report-misinformation-online
