Sort of company the Queen introduced to Republican politician (9)
I believe the answer is:
repertory
'sort of company' is the definition.
(as in a repertory theatre company)
'queen introduced to republican politician' is the wordplay.
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'introduced to' indicates putting letters inside.
'republican' becomes 'rep'.
'politician' becomes 'tory' (term for a Conservative Party politician).
'rep'+'tory'='reptory'
'er' going within 'reptory' is 'REPERTORY'.
'the' is the link.
(Other definitions for repertory that I've seen before include "Playhouse performing a regular stock of works" , "Collection" , "Type of theatre" , "performance" .)