Getting the current timestamp and compute the timestamp difference in minutes
Note that none of these suggestions will have any significant impact on the performance of your application overall. Don't micro-optimize performance until you have known, tested bottlenecks.

The getTimestamp() method is noise. If all you care about is the current timestamp in milliseconds, use System.currentTimeMillis().

You can use a constant to store the number of milliseconds in a minute, potentially saving the multiplication. Even if the compiler optimizes the math away, it's easier to read.

A java.sql.Timestamp is a kind of java.util.Date, and the getTime() method is defined there. Your method should accept a java.util.Date to support more clients at no cost.

Your method is poorly named. Something like getMinutesSince() would be more readable. Likewise, there are better variable names than what you've selected.

Use final to indicate that variables won't be reassigned. That reduces the cognitive load on the reader.

You don't really need as many variables as you have. You might even be able to get away with none and still have a reasonably clear method.

If you were to use all my suggestions, your code might look more like:

private static final long MILLISECONDS_PER_MINUTE = 60 * 1000;

public static long getMinutesSince(final java.util.Date startTime) {
  final long millisecondsSinceStart =
      System.currentTimeMillis() - startTime.getTime();
  return millisecondsSinceStart / MILLISECONDS_PER_MINUTE;
}