Blogger hasn't time for puzzle (5)
I believe the answer is:
poser
'for puzzle' is the definition.
(poser can mean a mystery or puzzle)
'blogger hasn't time' is the wordplay.
'blogger' becomes 'poster' (a blogger is someone who 'posts' online).
'hasn't' indicates named letters should be taken away.
'time' becomes 't' (abbreviation).
'poster' with 't' removed is 'POSER'.
(Other definitions for poser that I've seen before include "Tricky question" , "Spore raises a difficult question" , "Question; one trying to impress" , "Puzzling problem" , "Hard problem" .)