The word "play" has several different signs depending on what you mean.
If you mean play as in an "act" or a "drama," see: See: THEATER / act / play / drama
If you mean "play" as in "playing around" then you can use the version of this sign that shakes "Y" handshapes.
PLAY (as in "play time," "playing,")
Sample sentence: BASKETBALL, YOU LIKE PLAY? (Do you like to play basketball?)
0:00 / 0:00
PLAYER: To sign "player" simply add the "PERSON / AGENT" sign to the sign PLAY.
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PARTY: The sign PLAY happens to be one of the versions of the sign for "party." There are four common ways to sign "party." The point I want to make here though is that you should NOT initialize the sign play with a "P" hand.
See: PARTY
Notes:
I've observed quite a few educators of Deaf children using an initialized form of PLAY (with a "T" handshape) for the sign "TOYS." Which is to say, some of them do the sign for "toys" by signing "play" using "T" handshapes. I don't really think that is such a good idea. To me it looks sort of like "double bathroom" or something.
In context, the "Y" handshape version of the sign PLAY can be used to mean "toys" but I and most of my associates just spell "T-O-Y-S."
Notes: