Chilled about nature oddly showing dominance (7)
I believe the answer is:
control
'dominance' is the definition.
('control' can be a synonym of 'dominance')
'chilled about nature oddly' is the wordplay.
'chilled' becomes 'cool' ('cool' can be similar in meaning to 'chilled').
'about' is an insertion indicator.
'oddly' means one should take alternating letters.
The alternate letters of 'nature' are 'ntr'.
'cool' going around 'ntr' is 'CONTROL'.
'showing' is the link.
(Other definitions for control that I've seen before include "Check" , "Regulating device" , "Regulate; spymaster" , "Keep in line" , "Restraint" .)