Raise another case at the last minute (8)
I believe the answer is:
escalate
'raise' is the definition.
(thesaurus)
'another case at the last minute' is the wordplay.
'another' becomes 'e' (I've seen this in other clues).
'case at' becomes 'scala' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'last' indicates one should take the final letters.
The final letter of 'minute' is 'e'.
'e'+'scala'+'t'+'e'='ESCALATE'
Can you help me to learn more?
(Other definitions for escalate that I've seen before include "mount in tension" , "Increase in extent or intensity (8)V" , "Snowball" , "Magnify" , "Raise to higher level, perhaps war" .)