Royal cost includes new top (6)
I believe the answer is:
prince
'royal' is the definition.
(prince is a kind of royal)
'cost includes new top' is the wordplay.
'cost' becomes 'price' (the cost or price of something).
'includes' is an insertion indicator.
'top' suggests taking the first letters (in a down clue, the first letter is top).
The first letter of 'new' is 'n'.
'price' going around 'n' is 'PRINCE'.
(Other definitions for prince that I've seen before include "Son of a royal house" , "King's son" , "Possible future titular head" , "Pincer movement around the royal" , "Male heir to a throne" .)