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24a the Tabard Inn was the starting point (where they left )for the Canterbury Pilgrims; also a tunic

20a. (Princ) eton

Ivy League University Princeton (finishing letters )

Thanks, I should've got the Princeton one, but the others I had no idea about.

29a. Finish bowling with a side that's short facing one
END ON

1d. Delivery secures wicket before end of the game
BAGATELLE

17d. Outdated as a fairy cake might be?
MOTH-EATEN

Parses for the above please.

1d DELIVERY = BALL
WICKET = GATE
END OF TH(E) = E
BA GATE LL E

17d moth-eaten - outdated
Moth (fairy in Midsummer night's dream)
eaten - cake might be

Thanks, I didn't know that meaning of MOTH-EATEN.... I thought it was something that was in a poor condition rather than outdated.

Anyone worked out END ON?

Perhaps…
If you were to finish bowling to the on side, you could be said to END ON.
And, the short side of something pointing towards you is said to be END-ON (Chambers hyphenates this meaning)

Could be something else entirely of course.

Regarding moth-eaten, it can also mean antiquated/outdated, or well-worn in the sense of the usage of sayings etc.

5a. Cards that are left over, not initially used
TALON

8d. Steady note omitted by competitor
CONSTANT

13a. Do well as exiled Duke, having nothing to lose finally
PROSPER

16a. Shakespearean character hard to find in work by Lamb
OPHELIA

25a. Contact, perhaps, that's set up between banks
BRIDGE

6d. Mounting hesitation to put down furry animal
MUSQUASH

12a. Not beyond correction- go to expert
REPAIRABLE

17d. Drink is on the table where the score is kept
PEGBOARD

Parses for the above please.