Senile old bats surrounding rear of Windsor Castle, in which prince broods (8)
I believe the answer is:
elsinore
'castle in which prince broods' is the definition.
(home of Prince Hamlet in Shakespeare's play)
'senile old bats surrounding rear of windsor' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'bats' indicates anagramming the letters (slang for mad).
'surrounding' is an insertion indicator.
'rear of' says to take the final letters.
The final letter of 'windsor' is 'r'.
'senile'+'o'='senileo'
'senileo' anagrammed gives 'elsinoe'.
'elsinoe' placed around 'r' is 'ELSINORE'.
(Other definitions for elsinore that I've seen before include "Danish city" , "Tragic scene" , "Hamlet's home" , "haunted castle?" , "Danish port where Hamlet is set" .)