Carry out tours around area, running through (10)
I believe the answer is:
impalement
'running through' is the definition.
(to run through is to impale or skewer)
'carry out tours around area' is the wordplay.
'carry out' becomes 'implement' (synonyms).
'tours' means one lot of letters goes inside another (to tour can mean to go around).
'around area' becomes 'a' (maths abbreviation. I am not sure about the 'around' bit.).
'implement' going around 'a' is 'IMPALEMENT'.
Can you help me to learn more?
(Another definition for impalement that I've seen is " Running through".)