Short series of episodes involving leader in thrall of a government department (11)
I believe the answer is:
ministerial
'of a government department' is the definition.
'short series of episodes involving leader in thrall' is the wordplay.
'short series of episodes' becomes 'miniserial'.
'involving' is an insertion indicator.
'leader in' suggests taking the first letters.
The initial letter of 'thrall' is 't'.
'miniserial' placed around 't' is 'MINISTERIAL'.
(Other definitions for ministerial that I've seen before include "Relating to cabinet members" , "about government work" , "Maybe cabinet member's" .)