Hi Srikanth,

I trust you are doing very well.

Below is the sample code which I have tested in my org and it is working fine. Kindly modify the code as per your requirement.

Visualforce:

<apex:page standardController="Account" extensions="TestC">
    <apex:form >
        
        <apex:sectionHeader Title="Address Details" />
        <apex:pageBlock Title="Select the type of Address">
            
            <apex:pageBlockSection columns="1">
                <apex:PageBlockSectionItem >
                    <apex:outputLabel value="Address"/>                    
                    <apex:selectList id="id_1" value="{!Account.Rating}" size="1" >
                        <apex:actionSupport event="onchange" reRender="Container"/>
                        <apex:selectOptions value="{!items}"/>
                    </apex:selectList>                    
                </apex:PageBlockSectionItem>
                
                <apex:PageBlockSectionItem >                    
                    <apex:outputPanel id="Container" >
                        <apex:outputPanel id="ajaxrequest" rendered="{!Account.Rating!=''}" >
                            <apex:commandButton value="Continue"/>
                        </apex:outputPanel>           
                    </apex:outputPanel>
                </apex:PageBlockSectionItem>
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>

Controller:

public with sharing class TestC {
    
    private Account AD;
    
    public TestC(ApexPages.StandardController stdcontroller) {
        this.AD=(Account)stdController.getRecord();
    }
    
    Boolean disp=False;
    
    Public Boolean getdisp(){
        return disp;
    }
    
    String Values;
    
    public String getValues() {
        return Values;
    }
    
    public void setValues(String Values) {
        this.Values= Values;
        if(Values!=null)
            disp=True;
    }
    public List<SelectOption> getItems() {
        List<SelectOption> options = new List<SelectOption>();
        options.add(new SelectOption('None','None'));
        options.add(new SelectOption('CA','Cease Address'));
        options.add(new SelectOption('CANADA','Canada'));
        options.add(new SelectOption('MEXICO','Mexico'));
        return options;
    }
    
}

I hope it helps you.

Kindly let me know if it helps you and close your query by marking it as solved so that it can help others in future.

Thanks and Regards,
Khan Anas​