Cleric getting to grips with a particularly sensitive subject (7)
I believe the answer is:
reactor
'particularly sensitive subject' is the definition.
(somebody sensitive may react to things)
'cleric getting to grips with a' is the wordplay.
'cleric' becomes 'rector' (type of clergyman).
'getting to grips with' indicates putting letters inside.
'rector' going around 'a' is 'REACTOR'.
(Other definitions for reactor that I've seen before include "Nuclear power station core" , "power supplier" , "Apparatus for production of nuclear energy" , "device for generating energy" , "(Nuclear) powerplant" .)