If someone is allergic to cat, and they have a good friend who has a cat, and the friend has cat hair on them when away from cat, trigger allergy?

It can. Cat allergen is one of the most common allergens that is out there. It is easily transported on clothes of the owner to other locations. Cat allergen has been found just about everywhere even when there is not cat around.
Yes. Pet dander or the allergy-inducing components of pet skin and hair can stick to a pet owner's clothing and cause allergic reactions when pet-allergic people come in contact with the contaminated clothing or other items.