Transfer diamonds in royal house (4,4)
I believe the answer is:
hand over
'transfer' is the definition.
(I know that hand over is a more specific form of give)
'diamonds in royal house' is the wordplay.
'diamonds' becomes 'd' (abbreviation for the card suit diamonds).
'in' indicates putting letters inside.
'royal house' becomes 'Hanover' (Hanover is an example).
'd' going into 'hanover' is 'HAND OVER'.
(Other definitions for hand over that I've seen before include "Pass across; surrender" , "Yield possession of in overhand way" , "Deliver into control of another - in manual way?" , "Present or give to another person - manually?" , "Transfer" .)