Fair Isle is home to about 60 people. It has a primary school and nursery, a shop, post office and community hall.
It can be reached by sea or air from mainland Shetland.
The house that is available for let has oil heating, electricity supplied by the island’s renewable power schemes, a phone and internet services.
A croft is small holding and crofters share pasture land called common grazing for raising livestock.
People with knowledge of crofting and skills as an electrician, joiner or working with boats are among those being sought for the tenancy.
They would be asked to set up a business, or have an active role in Fair Isle knitwear – a textile developed on the island in the early 19th Century.
Angus Murray, NTS’ operations manager for Fair Isle, said: “We are looking forward to welcoming new people to the island to become part of the crofting community of Fair Isle.”
He added: “We are inviting resourceful and enthusiastic people with the skills, creativity, and care needed to make a success of this unique opportunity.”