Anchor adrift in my kingdom (8)
I believe the answer is:
monarchy
'kingdom' is the definition.
(I've seen this in another clue)
'anchor adrift in my' is the wordplay.
'adrift' indicates anagramming the letters.
'in' indicates putting letters inside.
'anchor' with letters rearranged gives 'onarch'.
'onarch' placed within 'my' is 'MONARCHY'.
(Other definitions for monarchy that I've seen before include "sort of government" , "Kingship system" , "Rule by a king or queen" , "kind of government" , "Rule by a sovereign" .)