Irresponsible pet restricting sleep regularly (8)
I believe the answer is:
careless
'irresponsible' is the definition.
('careless' can be similar in meaning to 'irresponsible')
'pet restricting sleep regularly' is the wordplay.
'pet' becomes 'caress' (I've seen this before**).
'restricting' is an insertion indicator.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'sleep' are 'le'.
'caress' going around 'le' is 'CARELESS'.
(Other definitions for careless that I've seen before include "Not careful or thorough enough" , "Incautious" , "Not paying enough attention" , "Inattentive to risk" , "Unconcerned; casual" .)