Sense dull person's in charge (5)
I believe the answer is:
logic
'sense' is the definition.
(I know that logic is a type of sense)
'dull person's in charge' is the wordplay.
'dull person' becomes 'log' (I can't explain this - if you can you should give a lot more credence to this answer).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'log'+'ic'='LOGIC'
Can you help me to learn more?
(Other definitions for logic that I've seen before include "Strict reasoning" , "method of reasoning" , "Rational thinking" , "Sound reasoning" , "this makes sense" .)