It depends.
You cannot claim Gift Aid if the membership fee is paid by an individual on someone else's behalf, unless they are minors.
If someone pays for membership for their child, who is under 18, you could claim Gift Aid on it, providing the normal conditions for claiming Gift Aid on membership fees are met.
Family memberships (e.g. buying membership for whole family a reduced cost) can have Gift Aid claimed on it as long as the normal conditions for claiming Gift Aid on membership fees are met.