Gradle sync project for newer libraries

I am new to Gradle and Android development.
How do I get Gradle to sync my project to use newer libraries?

I want to use setFragmentResultListener, which is available as of 1.3.0-alpha04, and its using 1.2.0.

My build.gradle file

apply plugin: 'com.android.application'

plugins {
    id 'java-library'
}

android {
    compileSdkVersion 30
    buildToolsVersion "30.0.1"

    defaultConfig {
        applicationId "com.hasgrok.communicator2"
        minSdkVersion 23
        targetSdkVersion 30
        versionCode 1
        versionName "1.0"

        testInstrumentationRunner "androidx.test.runner.AndroidJUnitRunner"
    }

    buildTypes {
        release {
            minifyEnabled false
            proguardFiles getDefaultProguardFile('proguard-android-optimize.txt'), 'proguard-rules.pro'
        }
    }
    compileOptions {
        sourceCompatibility JavaVersion.VERSION_1_8
        targetCompatibility JavaVersion.VERSION_1_8
    }
    dependenciesInfo {
        includeInApk true
        includeInBundle true
    }
}

dependencies {
    def core_version = "1.3.1"
    implementation "androidx.core:core:${core_version}"
    implementation fileTree(dir: "libs", include: ["*.jar"])
    implementation 'androidx.appcompat:appcompat:1.2.0'
    implementation 'androidx.constraintlayout:constraintlayout:2.0.0'
    implementation 'androidx.legacy:legacy-support-v4:1.0.0'
    implementation 'androidx.lifecycle:lifecycle-extensions:2.2.0'
    testImplementation 'junit:junit:4.13'
    androidTestImplementation 'androidx.test.ext:junit:1.1.1'
    androidTestImplementation 'androidx.test.espresso:espresso-core:3.2.0'
}

Yes, I know how to sync my project with Gradle files. I don't know how to get the library versions I'm looking for.

You'll sometimes get a lint warning (highlighted) telling you there's a newer version available, and you can use the quick-fix it suggests to update. You can also use the Project Structure window (under the File menu) and the Suggestions section will show you updates it knows about.

In this case, it's probably not suggesting the update to you, because you're currently on a stable release (1.2.0), and there's no update to that. 1.3.0-alpha04 is an unstable alpha release, which is treated as another, separate track. If you manually change it and start using an alpha version, it will suggest alpha updates to you instead

(you can do that if you want, just change the dependency text to exactly the name of the alpha release - but you might need to change other dependencies too, and expect things to break because that's what alphas are for!)

oh I just saw you're new to Android development. I would absolutely recommend not using any non-stable libraries, save yourself the headaches. There'll be another way to do whatever you want to use that new method for!

Goto File > Sync Project with Gradle Files