Increase when there's a botched case: dead (8)
I believe the answer is:
escalate
'increase' is the definition.
(escalating is a kind of increasing)
'a botched case dead' is the wordplay.
'a botched' indicates an anagram.
'dead' becomes 'late' ('late' can be similar in meaning to 'dead').
'case' is an anagram of 'esca'.
'esca'+'late'='ESCALATE'
'when there's' acts as a link.
(Other definitions for escalate that I've seen before include "Magnify" , "get high" , "Increase in magnitude" , "Amplify" , "Increase in intensity or extent, like trouble brewing" .)