Obscure publisher's hype lacking finish (4)
I believe the answer is:
blur
'obscure' is the definition.
(both can mean to vague or indistinct)
'publisher's hype lacking finish' is the wordplay.
'publisher's hype' becomes 'blurb' (promotional text from a publisher).
'lacking finish' means to remove the last letter.
'blurb' with its last letter removed is 'BLUR'.
(Other definitions for blur that I've seen before include "Make vague" , "Out-of-focus sight" , "Mist" , "murky spot" , "Group - smudge" .)