Restrains, checks, or cool-headedly rubs the wrong way (5)
I believe the answer is:
curbs
'restrains checks' is the definition.
'curbs' can be an answer for 'restrains' ('curb' can be a synonym of 'restrain'). I'm unsure of the 'checks' bit.
'cool-headedly rubs the wrong way' is the wordplay.
'cool-headedly' becomes 'c' (this might be a standard abbreviation I've not previously seen).
'the wrong way' indicates anagramming the letters (the letters in the wrong order).
'rubs' is an anagram of 'urbs'.
'c'+'urbs'='CURBS'
'or' acts as a link.
Can you help me to learn more?
(Other definitions for curbs that I've seen before include "Restrains" , "Place restrictions on" , "Keeps in check" .)