Inattentive PM's ashamed at heart when shown up (6)
I believe the answer is:
asleep
'inattentive' is the definition.
(I've seen this before)
'pm's ashamed at heart when shown up' is the wordplay.
'pm's' becomes 'Peel's' (19th-century prime minister Robert Peel).
'at heart' says to take the centre.
'when shown up' shows that the letters should be reversed in order.
The middle letter of 'ashamed' is 'a'.
'peels'+'a'='peelsa'
'peelsa' in reverse letter order is 'ASLEEP'.
(Other definitions for asleep that I've seen before include "Snoozing" , "In slumber" , "In the arms fo Morpheus" , "Please be at rest, oddly" , "Resting unconscious" .)