Royal household cool about second romance (9)
I believe the answer is:
courtship
'romance' is the definition.
(I've seen this before)
'royal household cool about second' is the wordplay.
'royal household' becomes 'court'.
'cool' becomes 'hip'.
'about' means one lot of letters go next to another.
'second' becomes 's' (common abbreviation).
'hip' put after 's' is 'ship'.
'court'+'ship'='COURTSHIP'
(Other definitions for courtship that I've seen before include "Wooing of a mate" , "In prosecution of suit" , "judicial craft?" , "Attempt to win" , "pursuit" .)