Conclusion of many old kings in royal house (4)
I believe the answer is:
york
'royal house' is the definition.
(I've seen this before)
'conclusion of many old kings' is the wordplay.
'conclusion of' says to take the final letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'kings' becomes 'RK' (R means rex - 'king' in Latin - and K means king).
The last letter of 'many' is 'y'.
'y'+'o'+'rk'='YORK'
'in' is the link.
(Other definitions for york that I've seen before include "Northern walled city" , "National Railway Museum city" , "A place" , "Whence the marching Grand Old Duke" , "Bowl out with ball pitching under bat" .)