Much depends on the land. Is it level? Is it well-drained? Has it got good soil?
Teh fact is, you'd have to do somethingwith it, as an acre left untended would soon become a wilderness of brambles and worse. The easiest thing to do is rent out to someone else to graze. Or you could sell the haylage/silage rights to a local farmer. Either way, grass needs to be managed, which includes keeping docks and thistles at bay and dressing the field with muck or fertiliser once a year.
If you want to invest your own effort, you can run your own pigs (buy in weaners and fatten them rather than breed - and rotate their pasture so that the whole acre doesn't become a quagmire).
You could keep chickens there. You could have two or three sheep (with all the buggerance that comes from keeping sheep!) You could raise a couple of beef steers for early slaughter.
You could grow a considerable amount of vegetable, including some exotics in a polytunnel or two.
But whatever you do will involve serious amounts of hard work. And, if you keep livestock other than poultry, you will have to register the land with your local animal health department to get a CPH holding number, and abide by the tagging and movement restrictions, and essentially become your own vet, plus you would have to ensure that you could have someone on site at least twice a day, 365 days a year.
Coppicing is good - you can get several tonnes an acre of willow or hazel, while chestnut is always in demand.
Get hold of a copy of John Seymour's book on self-sufficiency. A lot of it is idealistic twaddle, but it should give you some ideas of what you can do with an acre.