It's entirely up to individual employers. Some will restrict their graduate entry schemes solely to people who've graduated within the past year (or, if they allow for a post-study gap year, within the past two years). Others will accept other graduates.
However you need to be aware that some employers seem to have very rigid ideas about who they're looking for. A few years ago I saw a job advertised, which I knew I could do with one hand tied behind my back, which specified that applicants needed a relevant degree (which I had). It was a small company, so there was no 'graduate entry' scheme or 'graduate training programme'; they simply asked for a suitable degree.
I sent off for further details of that job, from which it became obvious that they were actually only seeking applicants who were in the final year of their studies. I could see no reason for that specification, other than age discrimination. (I'm in my fifties). I referred the matter to the Equality and Opportunities Commission but they were of the opinion that it would be hard to prove age discrimination since mature students who were completing their degree courses were not excluded from applying.
So you might find that you're already subject to indirect age discrimination.
Chris