Lady with pet moving expertly (7)
I believe the answer is:
adeptly
'expertly' is the definition.
(thesaurus)
'lady with pet moving' is the wordplay.
'with' means one lot of letters go next to another.
'moving' is an anagram indicator (letters are moved around).
'lady' put after 'pet' is 'petlady'.
'petlady' with letters rearranged gives 'ADEPTLY'.
(Other definitions for adeptly that I've seen before include "with great skill" , "In a proficient manner" , "Skilfully" , "How experts act" , "Showing skill" .)