The Odin Project - Project Ruby: Translating from English to Pig Latin
Some notes:


expect(translate("three")).to eq("eethray"). Be consistent, use always a local variable or don't. I think this way looks pretty cool.
Isn't the code inside a module/class?
translate. This methods is unnecessarily verbose. You don't need to check if there is a space or not, since the algorithm works just the same if there is not. 
Those two nexts are redundant.
rearrange: This method would look so much nicer if you don't use imperative style. 
If a regular expression can express the rules, you should consider using it. It will be easier to read and much more compact.
Side note: The rules are pretty simple. If they ever get more complex, a manual processing will be undecipherable and regexps will come short. Then you'll need something more sophisticated, like a parser (i.e. grammy).


I'd write:

def translate(phrase)
  phrase.split(" ").map { |word| rearrange(word) }.join(" ") 
end

def rearrange(word)
  match = word.match(/^((?:qu|[bcdfghjklmnpqrstvwxz])*)(.*)$/)
  match ? match[2] + match[1] + "ay" : word
end


If you have trouble reading that regular expressions, consider using multi-line regexps with named captures:

def rearrange(word)
  match = word.match(%r{
    ^
    (?&lt;leading_consonants&gt;(?:qu|[bcdfghjklmnpqrstvwxz])*) 
    (?&lt;rest&gt;.*)
    $)
  match ? match[:rest] + match[:leading_consonants] + "ay" : word
end