Find the red-and-white SELL stall in the plaza near the shop and open its sale menu.
Check the summary above the cards: it lists how many barbers can be sold and their combined cash value. A barber must be unlocked and unequipped to be eligible. Dimmed cards marked IN USE are protected, even when a price appears beneath them.
To sell a current worker, select that barber in BARBERS and choose UNEQUIP first. For help choosing a replacement, use the lineup guide.