Sick young woman injecting drug that's unlawful (7)
I believe the answer is:
illegal
'unlawful' is the definition.
('illegal' can be similar in meaning to 'unlawful')
'sick young woman injecting drug' is the wordplay.
'sick' becomes 'ill' ('ill' can be a synonym of 'sick').
'young woman' becomes 'gal' ('gal' can be a synonym of 'young woman').
'injecting' is an insertion indicator.
'drug' becomes 'e' (e is another name for ecstasy).
'ill'+'gal'='illgal'
'illgal' placed around 'e' is 'ILLEGAL'.
'that's' is the link.
(Other definitions for illegal that I've seen before include "Unlawful" , "Not allowed" , "crooked" , "Not lawful" , "Not in conformity with law" .)