F. R. Leavis was a real-world scholar and literary critic, but A. S. Byatt inserts a fictionalized version of him into Possession to give extra depth and texture to the novel's descriptions of James Blackadder's undergraduate experience.
The F. R. Leavis who appears in the novel is arrogant and overly confident in his own expertise. As the narrator puts it:
Leavis did to Blackadder what he did to serious students; he showed him the terrible, the magnificent importance and urgency of English literature and simultaneously deprived him of any confidence in his own capacity to contribute to, or change it. The young Blackadder wrote poems, imagined Dr Leavis's comments on them, and burned them. (3.15)
Sounds like a fun guy to work with…
You might be interested to know that Byatt is actually drawing on some of her own experiences here. As she says in an interview with Philip Hensher:
Leavis was a very important figure for me in the sense that I perceived him as a kind of blockage to everybody who wanted to do what I wanted to do. […] I went to two of his seminars, which, you know, is a story I have told in Possession—I decided I wasn't going to go to any more because either I would get like the other people who worshipped him, who derived an enormous amount from him, but somehow didn't make anything, or I would just get angrier and angrier with what I saw as his manipulation of his students into admiring him. (Source.)
Looks like Byatt got the last laugh.