Cast not hotter in Succession (2,3,4)
I believe the answer is:
on the trot
'in succession' is the definition.
(I've seen this before)
'cast not hotter' is the wordplay.
'cast' indicates an anagram (letters are dispersed or cast around).
'not'+'hotter'='nothotter'
'nothotter' with letters rearranged gives 'ON THE TROT'.
(Other definitions for on the trot that I've seen before include "Where orthodox Stalinist hurled anathemas" , "One after another" , "Moving at a fairly fast pace" , "Informally busy like slow run" , "running" .)