Author's first book about hospital reception (2-4)
I believe the answer is:
at-home
'reception' is the definition.
(at home is a kind of reception)
'author's first book about hospital' is the wordplay.
'author's first' becomes 'a' (1st letter of 'author').
'book' becomes 'tome' (a tome is a book).
'about' indicates putting letters inside.
'hospital' becomes 'H' (abbreviation for hospital on maps).
'tome' going around 'h' is 'thome'.
'a'+'thome'='AT-HOME'
(Other definitions for at-home that I've seen before include "Not away, ready for visitors" , "Oh mate! (anag)" , "Reception at residence" , "Former Italian currency" , "In (for a party?)" .)