Nan regularly drew up close to Her Majesty (8)
I believe the answer is:
grandeur
'majesty' is the definition.
(both can mean greatness or splendour)
'nan regularly drew up close to her' is the wordplay.
'nan' becomes 'gran' (I've seen this before).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'close to' indicates one should take the final letters (the close of something is the end).
The last letter of 'her' is 'r'.
'drew'+'up'='drewup'
The alternate letters of 'drewup' are 'deu'.
'gran'+'deu'+'r'='GRANDEUR'
(Other definitions for grandeur that I've seen before include "The splendour of France" , "Greatness, perhaps ironic" , "Magnificence - rare dung (anag)" , "Majesty (God's, Hopkins)" , "Impressive splendour" .)