I'll do a few "goes" to give you the idea - the bits in brackets are "in your mind":
1st player: posts "Road Runner"
2nd player: [thinks of a phrase that starts with "runner" and adds a new word to make the next phrase, say, "runner bean"] but posts "bean salad"
3rd player: [thinks "salad days"] posts "days past"
3rd player: [thinks "past glory"] posts "Glory Road" (titles etc permitted)
4th player: [thinks "road works"] posts "works party"
See, its easy, and only twice the work

So . . .
I'll offer this for the real starter:
Tyrannosaurus Rex