Explosive anger curtailed inside: it's touching (7)
I believe the answer is:
tangent
'touching' is the definition.
(I've seen this before)
'explosive anger curtailed inside' is the wordplay.
'explosive' becomes 'tnt' (TNT is an example).
'curtailed' means to remove the last letter.
'inside' indicates putting letters inside.
'anger' with its final letter removed is 'ange'.
'tnt' placed around 'ange' is 'TANGENT'.
'it's' acts as a link.
(Other definitions for tangent that I've seen before include "Straight line that touches but does not intersect a curve" , "At which one can go off" , "Line touching circumference" , "Straight line just touching a curve" , "Line that touches curve without crossing it" .)