Cousins, terribly irrational in misgiving (9)
I believe the answer is:
suspicion
'misgiving' is the definition.
(I know that misgiving can be written as suspicion)
'cousins terribly irrational in' is the wordplay.
'terribly' is an anagram indicator.
'irrational' becomes 'pi' (an irrational number).
'in' indicates putting letters inside.
'cousins' is an anagram of 'suscion'.
'suscion' enclosing 'pi' is 'SUSPICION'.
(Other definitions for suspicion that I've seen before include "Misgiving, doubt" , "Trace" , "Hitchcock classic" , "Inkling" , "Cautious distrust" .)