TWA always had very artistic, intricate travel posters.
My guess is that this one is from the mid 1950's.
Here is a wonderful website with tons of information about the aviation giant, told from the flight attendants' point of view. Tons of pictures and information.
Sadly, when American Airlines acquired Trans World in 2001, all of the TWA flight attendants were fired, regardless of their tenure. This was the exact opposite of what American Airlines management had promised to do. "Doing what they do best," I guess.