A learner falling short — the first person to go under in this world? (7)
I believe the answer is:
academe
'this world?' is the definition.
(academe is a kind of world)
'a learner falling short the first person to go under' is the wordplay.
'learner' becomes 'cadet' (cadet can mean a trainee).
'falling short' means to remove the last letter.
'the first person' becomes 'me' (first-person pronoun).
'to go under' says to put letters next to each other (in a down clue, some letters go below others).
'cadet' with its final letter taken off is 'cade'.
'a'+'cade'+'me'='ACADEME'
'in' is the link.
(Other definitions for academe that I've seen before include "The world of education" , "University environment" , "learned environment" , "The world of teaching" , "The scholarly world" .)