Complete, however approximate (8)
I believe the answer is:
thorough
'complete' is the definition.
(I know that complete can be written as thorough)
'however approximate' is the wordplay.
'however' becomes 'tho'' (I've seen this in another clue).
'approximate' becomes 'rough' (I've seen this before).
'tho'+'rough'='THOROUGH'
(Other definitions for thorough that I've seen before include "Attending to every detail - complete" , "Miticulous or exhaustive" , "Complete, absolute" , "Doing things with great attention to detail" , "Attentive to detail" .)