Look Al up, girl! (4)
I believe the answer is:
lola
'girl' is the definition.
'look al up' is the wordplay.
'look' becomes 'lo'.
'up' says the letters should be written backwards (in down clue: letters go upwards).
'al' reversed gives 'la'.
'lo'+'la'='LOLA'
(Other definitions for lola that I've seen before include "song by 4 [THE KINKS]" , "Whatever -- wants (song); -- Montez, mistress of Ludwig I" .)