You need two formats: one to parse, and one to format. You need to parse from String to Date with one DateFormat, then format that Date into a String with the other format.
Currently, your single SimpleDateFormat is half way between - you've got HH which is 24-hour, but you've also got aa which is for am/pm. You want HH without the aa for input, and hh with the aa for output. (It's almost never appropriate to have both HH and aa.)
TimeZone utc = TimeZone.getTimeZone("etc/UTC");
DateFormat inputFormat = new SimpleDateFormat("dd MMM, yyyy HH:mm",
Locale.US);
inputFormat.setTimeZone(utc);
DateFormat outputFormat = new SimpleDateFormat("dd MMM, yyyy hh:mm aa",
Locale.US);
outputFormat.setTimeZone(utc);
Date date = inputFormat.parse(input);
String output = outputFormat.format(date);
Note that I'm setting the locale to US so it can always parse "Nov", and the time zone to UTC so you don't need to worry about certain times being skipped or ambiguous.