Post you’d not want in Cheltenham for one minute! (4)
I believe the answer is:
spam
'post you'd not want in cheltenham' is the definition.
I can't tell whether this defines the answer.
'one minute' is the wordplay.
'one' becomes 'spa' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'minute' becomes 'm' (abbreviation).
'spa'+'m'='SPAM'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for spam that I've seen before include "Unwelcome approach" , "unwanted delivery" , "email messages" , "canned meat" , "Possible item from menu" .)