Girl that’s lifted bible getting into trouble (5)
I believe the answer is:
avril
'girl' is the definition.
'lifted bible getting into trouble' is the wordplay.
'lifted' shows that the letters should be reversed in order (going up in down clue).
'bible' becomes 'rv' (Revised Version, revision of King James Bible).
'getting into' means one lot of letters goes inside another.
'trouble' becomes 'ail' (synonyms).
'rv' written backwards gives 'vr'.
'vr' inserted within 'ail' is 'AVRIL'.
'that's' acts as a link.
(Other definitions for avril that I've seen before include "Nice girl" , "French for April" .)