Lax bloke with broken leg in Northern Ireland (9)
I believe the answer is:
negligent
'lax' is the definition.
('negligent' can be similar in meaning to 'lax')
'bloke with broken leg in northern ireland' is the wordplay.
'bloke' becomes 'gent' (I've seen this in other clues**).
'with' is a charade indicator (letters next to each other).
'broken' is an anagram indicator.
'in' indicates putting letters inside.
'northern ireland' becomes 'ni'.
'leg' anagrammed gives 'egl'.
'egl' inserted within 'ni' is 'negli'.
'gent' put after 'negli' is 'NEGLIGENT'.
(Other definitions for negligent that I've seen before include "sloppy" , "Lax" , "lacking care" , "Of the study of insects" , "Careless, remiss" .)