Careless chap supports wobbly Nigel (9)
I believe the answer is:
negligent
'careless' is the definition.
(similar in meaning)
'chap supports wobbly nigel' is the wordplay.
'chap' becomes 'gent' (I've seen this in other clues).
'supports' means one lot of letters go next to another (bottom letters provide a support for the top ones).
'wobbly' is an anagram indicator (I've seen this in other clues).
'nigel' anagrammed gives 'negli'.
'gent' after 'negli' is 'NEGLIGENT'.
(Other definitions for negligent that I've seen before include "Careless, remiss" , "Lax" , "slack" , "Not taking due care" , "Failing to take proper care" .)