Bet grunge fan is the first to print (9)
I believe the answer is:
gutenberg
'the first to print' is the definition.
I can't judge whether this definition defines the answer.
'bet grunge fan' is the wordplay.
'fan' is an anagram indicator (I've seen 'fanned' mean this (I've seen this in other clues)).
'bet'+'grunge'='betgrunge'
'betgrunge' with letters rearranged gives 'GUTENBERG'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for gutenberg that I've seen before include "Pioneer printer" , "German printer of a 15th century Bible" , "German printing pioneer" , "Publisher" , "He invented movable-type printing" .)