Party on right love your old girl (7)
I believe the answer is:
dorothy
'girl' is the definition.
'party on right love your old' is the wordplay.
'party' becomes 'do' (do is a kind of party).
'on' means one lot of letters go next to another.
'right' becomes 'r' (common abbreviation).
'love' becomes 'o' (In tennis, 'love' means 'zero').
'your old' becomes 'thy'.
'do'+'r'+'o'+'thy'='DOROTHY'
(Other definitions for dorothy that I've seen before include "one of 5d's troupe" , "Wizard of Oz child" , "Girl from Kansas" , "Female" , "'Wizard of Oz' girl" .)