0 to look after a child as part of your family for a time, without becoming their legal parent -- affiliare, prendere in affidamento
1 to look after for a period of time; to bring up a child that is not one’s own -- allevare
She fostered the children for several months.
2 to encourage or give help to (ideas etc) -- incoraggiare, favorire
She fostered the child’s talents.