Noted diarist? Yes, frantically penning page after page (5)
I believe the answer is:
pepys
'noted diarist?' is the definition.
(I've seen this in another clue)
'yes frantically penning page after page' is the wordplay.
'frantically' indicates an anagram.
'penning' is an insertion indicator.
'page' becomes 'p'.
'after' says to put letters next to each other.
'page' becomes 'p'.
'yes' is an anagram of 'eys'.
'eys' going around 'p' is 'epys'.
'epys' put after 'p' is 'PEPYS'.
(Other definitions for pepys that I've seen before include "Samuel -, English diarist" , "London diarist" , "English civil servant and diarist, d. 1703" , "Journalist" , "Samuel -, seventeenth century diarist" .)