Suspect's name associated with signs of debt (7)
I believe the answer is:
dubious
'suspect's' is the definition.
(I've seen this before)
'name associated with signs of debt' is the wordplay.
'name' becomes 'dub' (as in dubbing someone with a particular name).
'associated with' means one lot of letters go next to another.
'signs of debt' becomes 'IOUs' (IOU's or I Owe You's).
'dub'+'ious'='DUBIOUS'
(Other definitions for dubious that I've seen before include "unreliable" , "Unsure, unconvinced" , "Uncertain - suspect" , "Of questionable value" , "Open to suspicion" .)