Playing with the musical turtle
Java 8, 48 39 33 bytes

s-&gt;&quot;ROYGBRO BGYORBG&quot;.indexOf(s)|7

-6 bytes thanks to @RickHitchcock, so make sure to upvote him as well!
Takes uppercase color as input-String. Outputs -1 for none, 7 for clockwise, and 15 for counterclockwise.
Try it online.
Explanation:
s-&gt;      // Method with String parameter and integer return-type
   &quot;ROYGBRO BGYORBG&quot;.indexOf(s)
         //  Get the index of the input in the String &quot;ROYGBRO BGYORBG&quot;,
         //  which will result in -1 if the input is not a substring of this String
    |7   //  Then take a bitwise-OR 7 of this index, and return it as result


Old 39 bytes answer:
s-&gt;(char)&quot;ROYGBRO BGYORBG&quot;.indexOf(s)/7

Takes uppercase color as input-String. Outputs 9362 for none, 0 for clockwise, and 1 for counterclockwise.
Try it online.
Explanation:
s-&gt;      // Method with String parameter and integer return-type
   (char)&quot;ROYGBRO BGYORBG&quot;.indexOf(s)
         //  Get the index of the input in the String &quot;ROYGBRO BGYORBG&quot;,
         //  which will result in -1 if the input is not a substring of this String
         //  And cast it to a char (-1 becomes character with unicode value 65535)
    /7   //  Integer-divide it by 7 (the char is implicitly converted to int doing so)