no sooner said than done Definition

sooner
adverb

1. Earlier than previously thought.
2. Preferably.

Example: I'd sooner die than go back there

Idiom: no sooner ... than ...

Immediately after ... then ....
Example: No sooner had I mentioned his name than he appeared

Idiom: no sooner said than done

Said of a request, promise, etc: immediately fulfilled.

Idiom: sooner or later

Eventually.