Careless, eccentric uncle left without paying ultimately (10)
I believe the answer is:
neglectful
'careless' is the definition.
(thesaurus)
'eccentric uncle left without paying ultimately' is the wordplay.
'eccentric' is an anagram indicator.
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'ultimately' says to take the final letters.
The last letter of 'paying' is 'g'.
'uncle'+'left'='uncleleft'
'uncleleft' anagrammed gives 'nelectful'.
'nelectful' placed around 'g' is 'NEGLECTFUL'.
(Other definitions for neglectful that I've seen before include "Not taking proper care" , "Careless" , "Giving insufficient care" , "Sloppy" , "remiss" .)