Straightway, forthwith; there on the spot.

With after: immediately following (an event, often a meal).

In combination with after (or hereafter, thereafter, etc.), forming adverbial or prepositional phrases with the sense ‘directly or immediately…

at (the) next: in the immediate vicinity; (also) without an intermediary, directly. Obsolete.

Immediately following upon this (in time or consequence).

In the next place; immediately afterwards.

As soon as that happened, was done, or was said; immediately after that; = thereupon, adv. 2b.

Upon that (in time or order); on that being done or said; (directly) after that.

Directly or next after that; at the next moment; immediately afterwards; then, thereupon; = since, adv. 1 (Occasionally strengthened by after.)

Then, thereupon; immediately afterwards.

In the next place; next.

Of immediately subsequent or consequent action (on, prep. 9). Now more usually whereupon, adv. 4.