School initially put me up before I got home (4)
I believe the answer is:
semi
'home' is the definition.
(short for semi-detached)
'school initially put me up before i' is the wordplay.
'initially' suggests taking the first letters.
'put' is a charade indicator (letters next to each other).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'before' says to put letters next to each other.
The initial letter of 'school' is 's'.
'me' back-to-front is 'em'.
's'+'em'+'i'='SEMI'
'got' acts as a link.
(Other definitions for semi that I've seen before include "House sharing a wall" , "accommodation" , "The last but one round" , "eg Half a house" , "The next to final round" .)