Complicated ruling on breathing apparatus (4,4)
I believe the answer is:
iron lung
'breathing apparatus' is the definition.
(iron lung is a kind of breathing apparatus)
'complicated ruling on' is the wordplay.
'complicated' indicates anagramming the letters (a complex or confusing ordering of the letters).
'ruling'+'on'='rulingon'
'rulingon' with letters rearranged gives 'IRON LUNG'.
(Other definitions for iron lung that I've seen before include "Rigid case fitting over body for artificial respiration" , "Artificial respirator" , "breather" , "Artificial respiration chamber" , "Cylinder used in treating polio" .)