Begin to accommodate first of undergraduates in royal house (6)
I believe the answer is:
stuart
'royal house' is the definition.
(royal house of Scotland and England)
'begin to accommodate first of undergraduates' is the wordplay.
'begin' becomes 'start' (synonyms).
'to accommodate' means one lot of letters goes inside another.
'first of undergraduates' becomes 'u' (1st letter of 'undergraduates').
'start' placed around 'u' is 'STUART'.
'in' is the link.
(Other definitions for stuart that I've seen before include "Scottish royal dynasty" , "C17 royal house" , "Former royal house" , "Member of royal family" , "Scottish royal family" .)