Hurried ahead, being unreasonably rude about the hush (6)
I believe the answer is:
rushed
'hurried ahead' is the definition.
'rushed' can be an answer for 'hurried' ('rush' can be a synonym of 'hurry'). I am not certain of the 'ahead' bit.
'unreasonably rude about the hush' is the wordplay.
'unreasonably' indicates anagramming the letters.
'about' is an insertion indicator.
'the hush' becomes 'sh'.
'rude' anagrammed gives 'rued'.
'rued' placed around 'sh' is 'RUSHED'.
'being' is the link.
Can you help me to learn more?
(Other definitions for rushed that I've seen before include "Done in a hurry" , "stampeded" , "done too quickly" , "Moved with urgent haste" , "Was quick" .)