Get annoyed with stone enclosing most of burial place (9)
I believe the answer is:
aggravate
'get annoyed' is the definition.
(to aggravate someone is to get them annoyed)
'stone enclosing most of burial place' is the wordplay.
'stone' becomes 'agate' (agate is a type of stone).
'enclosing' is an insertion indicator.
'most of' means to remove the last letter.
'burial place' becomes 'grave' (I've seen this before).
'grave' with its final letter taken away is 'grav'.
'agate' going around 'grav' is 'AGGRAVATE'.
'with' is the link.
(Other definitions for aggravate that I've seen before include "compound" , "Make (a problem) worse" , "Make a bad situation worse" , "Make more serious" , "Worsen" .)