Probably you should just set TimeZone to your environment and in general you should avoid using the old java.util.Date
class.
If you are running on java 8 or above, you can use similar code to display the time in desired time zone.
<textField>
<reportElement x="0" y="0" width="100" height="30" uuid="ac702c94-69e5-4439-9d32-3c944119dbe6"/>
<textFieldExpression>
<![CDATA[java.time.format.DateTimeFormatter.ofPattern("dd-MMM-yyyy HH:mm").
withZone(java.time.ZoneId.of("Asia/Calcutta")).format($P{START_DATE}.toInstant())]]>
</textFieldExpression>
</textField>
If you are not on java 8 you can use libraries like ThreeTen-Backport or Joda-Time to have this functionality.
Full example with different zoneId on same java.util.Date
jrxml
<?xml version="1.0" encoding="UTF-8"?>
<jasperReport xmlns="http://jasperreports.sourceforge.net/jasperreports" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://jasperreports.sourceforge.net/jasperreports http://jasperreports.sourceforge.net/xsd/jasperreport.xsd" name="TimeZone" pageWidth="595" pageHeight="842" whenNoDataType="AllSectionsNoDetail" columnWidth="555" leftMargin="20" rightMargin="20" topMargin="20" bottomMargin="20" uuid="b3143043-a16b-43db-81c4-6313b0d4922c">
<parameter name="START_DATE" class="java.util.Date">
<defaultValueExpression><![CDATA[new java.util.Date()]]></defaultValueExpression>
</parameter>
<queryString>
<![CDATA[]]>
</queryString>
<title>
<band height="60" splitType="Stretch">
<staticText>
<reportElement x="0" y="0" width="150" height="20" uuid="a0353412-1861-4c12-ac26-b40a6768a88c"/>
<textElement textAlignment="Center" verticalAlignment="Middle">
<font isBold="true"/>
</textElement>
<text><![CDATA[America/New_York]]></text>
</staticText>
<staticText>
<reportElement x="150" y="0" width="150" height="20" uuid="28b938b9-d117-4447-91d2-b5bb9334bad6"/>
<textElement textAlignment="Center" verticalAlignment="Middle">
<font isBold="true"/>
</textElement>
<text><![CDATA[Europe/Rome]]></text>
</staticText>
<staticText>
<reportElement x="300" y="0" width="150" height="20" uuid="adceb53f-555d-4be3-bd1e-c9d55b90d90d"/>
<textElement textAlignment="Center" verticalAlignment="Middle">
<font isBold="true"/>
</textElement>
<text><![CDATA[Asia/Calcutta]]></text>
</staticText>
<textField>
<reportElement x="0" y="20" width="150" height="20" uuid="ebf48192-f394-447b-8264-e66c56289f54"/>
<textElement textAlignment="Center" verticalAlignment="Middle"/>
<textFieldExpression><![CDATA[java.time.format.DateTimeFormatter.ofPattern("dd-MMM-yyyy HH:mm").withZone(java.time.ZoneId.of("America/New_York")).format($P{START_DATE}.toInstant())]]></textFieldExpression>
</textField>
<textField>
<reportElement x="150" y="20" width="150" height="20" uuid="ebf48192-f394-447b-8264-e66c56289f54"/>
<textElement textAlignment="Center" verticalAlignment="Middle"/>
<textFieldExpression><![CDATA[java.time.format.DateTimeFormatter.ofPattern("dd-MMM-yyyy HH:mm").withZone(java.time.ZoneId.of("Europe/Rome")).format($P{START_DATE}.toInstant())]]></textFieldExpression>
</textField>
<textField>
<reportElement x="300" y="20" width="150" height="20" uuid="ac702c94-69e5-4439-9d32-3c944119dbe6"/>
<textElement textAlignment="Center" verticalAlignment="Middle"/>
<textFieldExpression><![CDATA[java.time.format.DateTimeFormatter.ofPattern("dd-MMM-yyyy HH:mm").withZone(java.time.ZoneId.of("Asia/Calcutta")).format($P{START_DATE}.toInstant())]]></textFieldExpression>
</textField>
</band>
</title>
</jasperReport>
Output
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…