Shut up about a Tory leader being inexperienced (8)
I believe the answer is:
immature
'inexperienced' is the definition.
('immature' can be similar in meaning to 'inexperienced')
'shut up about a tory leader' is the wordplay.
'shut up' becomes 'immure' (I've seen this in other clues).
'about' indicates putting letters inside.
'tory leader' becomes 't' (I've seen this in other clues).
'a'+'t'='at'
'immure' placed around 'at' is 'IMMATURE'.
'being' is the link.
(Other definitions for immature that I've seen before include "Not yet adult or fully developed" , "Not yet fully-developed" , "Undeveloped - unripe" , "Not fully ripe or developed" , "Like childish behaviour" .)