Me and Her Majesty to ramble (7)
I believe the answer is:
meander
'ramble' is the definition.
(I know that ramble can be written as meander)
'me and her majesty' is the wordplay.
'her majesty' becomes 'ER' (Elizabeth Regina).
'me'+'and'+'er'='MEANDER'
'to' acts as a link.
(Other definitions for meander that I've seen before include "Wandering direction" , "circuitous route" , "windy" , "keep dodging the point" , "Aimless course" .)