Can we play "ready golf" in a club medal, or is there a penalty for playing out of turn?

In stroke play (medals and Stablefords) there is no penalty for playing out of turn, and players are allowed and encouraged to play "ready golf", out of turn in a safe and responsible way.

The normal order is:

• First tee: the order of the draw (or by agreement or a random method if there's no draw).
• Other tees: the lowest gross score on the previous hole has the honour, even in a handicap competition.
• After teeing off: the ball farthest from the hole is played first.

The one exception: if two or more players agree to play out of turn to give one of them an advantage, and one of them does, each player who agreed gets two penalty strokes.

In match play, order matters: if you play out of turn, your opponent may cancel the stroke and make you play again.

Source: Rules of Golf (2023), Rule 6.4.