What does/did Irish playwright and novelist Samuel Beckett have in common with Warwickshire's greatest ever all-rounder, Frank Foster?

Tricky question - were they both left arm quicks?

Congratulations! You win the (non-existent) prize.
Samuel Beckett played two first-class cricket matches for Dublin University against Northants as a fast-medium left arm bowler, just like Frank Foster. I suspect that whereas Foster was more fast than medium, Beckett was more medium than fast.
The other oddity is that it is just possible that they met. When poor Frank Foster was in the mental hospital where he spent the last ten years of his life, one of the other inmates was Lucia Joyce, the daughter of James Joyce. Samuel Beckett had been in a relationship with her and it is known that he visited her at the hospital. So in my imagination, he and Frank Foster met there on one of his visits and compared notes about left arm quick bowling.
Anyway, back to reality!

'Tiger' Smith used to stand up to Foster so I am not sure just how 'Fast' he would have been even though Smith was a Test wicket-keeper. The book on Foster by Robert Brooke, 'And The Fields Were Sudden Bare' is an excellent read and a great insight into how used and abused cricketers were before WW1.

I agree that Robert Brooke's book is a great read.
As for Foster's speed, his reputation was that he gained pace off the pitch and he was tall by the standards of the day so got plenty of bounce. So I would say he was lively rather than genuinely fast. He was very accurate which made it easier for "TIger" to stand up to him.