Run in manner that's suspicious (4)
I believe the answer is:
wary
'suspicious' is the definition.
(thesaurus)
'run in manner' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'in' is an insertion indicator.
'manner' becomes 'way' ('way' can be a synonym of 'manner').
'r' inserted inside 'way' is 'WARY'.
'that's' acts as a link.
(Other definitions for wary that I've seen before include "James Bond villain" , "Cautious and vigilant.17 Add up for infant" , "Watchful" , "Cautious, suspicious" , "Distrustful" .)