Privately friendly, hugging Queen and heir (10)
I believe the answer is:
personally
'privately' is the definition.
(thesaurus)
'friendly hugging queen and heir' is the wordplay.
'friendly' becomes 'pally' ('pally' can be similar in meaning to 'friendly').
'hugging' means one lot of letters goes inside another.
'queen' becomes 'er' (abbreviation for Elizabeth Regina).
'and' means one lot of letters go next to another.
'heir' becomes 'son' (I've seen this before).
'er'+'son'='erson'
'pally' enclosing 'erson' is 'PERSONALLY'.
(Other definitions for personally that I've seen before include "as far as one is concerned" , "in my opinion" , "in my book" , "I think" , "Speaking for myself" .)