What would you like help with regarding this skin patch, for example possible causes, home care, or whether it needs medical review?

It most looks like hand eczema (contact or irritant dermatitis): a dry, thickened, scaly patch caused or worsened by frequent washing, detergents, sanitizer, sweating, friction, gloves, or an allergy to something contacting the skin. The appearance of thick, rough, flaky skin fits this pattern, although a photo cannot confirm it. The AAD description of hand eczema similarly notes dry, thick, scaly, sometimes painful hand skin.

A fungal infection of the hand (tinea manuum) is another possibility, particularly if it is mainly on one hand and you also have peeling/itching between the toes or athlete's foot. It needs an in-person examination, sometimes a simple skin scraping, because steroid creams alone can worsen or hide fungal infection.

Until assessed:

See a clinician or dermatologist if it is spreading, very itchy/painful, cracked or bleeding, oozing, warm/swollen, or not improving within 1-2 weeks.