How to checkout and build maven project from gradle?

Unfortunately, there is no common way to do this out-of-the-box, but you can reach this with custom tasks:

Extract maven package

task extractMavenPackage(type: Copy){
  destinationDir file(mvnHomeDir)
  from zipTree(configurations.maven.singleFile)
  includeEmptyDirs = false
  eachFile {  // workaround to skip first-level folder
    List segments = it.relativePath.segments as List
    it.path = segments.tail().join('/')
  }
}

Execute build

task mvnCleanPackage(type: Exec) {
  dependsOn extractMavenPackage, extractZeppelinSources
  commandLine "${mvnHomeDir}/bin/mvn.bat"
  workingDir zeppelinProjectDir
  args "-T", "4"
  // args "-s", "$projectDir/settings.xml" // uncomment it if you want to provide custom settings.xml
  args "clean", "package"
  args "-DskipTests"
  args "-P", "build-distr"
  args "-Phadoop-2.6", "-Dhadoop.version=2.6.0", "-Dhbase.hbase.version=1.2.0", "-Dhbase.hadoop.version=2.6.0"
}

See full example on maven-from-gradle-example github project