There are two ways to run another build in your current build.
Option 1: add PowerShell task in your current build definition to queue another build by REST API
Assume another build id is 5, so you can add PowerShell task with the script:
$body = @{
definition = @{
id = 5
}
}
$Uri = "http://account.visualstudio.com/DefaultCollection/project/_apis/build/builds?api-version=2.0"
$buildresponse = Invoke-RestMethod -Method Post -UseDefaultCredentials -ContentType application/json -Uri $Uri -Body (ConvertTo-Json $body)
Option 2: install related extension in Market place
There are some extensions you can install for your VSTS account, then you can add the task to queue another build. such as Queue Build(s) Task, Trigger New Build, Queue New Build etc.