The PnP game used to allow you to 'hold' or delay your action until later in the round. I think that's what the OP is referring to.
I believe this was scrubbed for 5e because it was being abused by players under the effect of 'until your next turn'-type spells and effects. It makes sense for me, going first is not always a benefit and having a higher initiative should always be an advantage.
Holding your action is still a thing in 5e, I can't remember the exact wording off the top of my head, but it is specifically an action you prepare that then uses your reaction to trigger if the circumstances are met, otherwise it just eats up your action and nothing happens if it's not met. This is painful if you try and do a spell this way, as if you hold your action for casting a spell and the action is never triggered, any resources consumed in the casting of the spell (e.g spell slots) are still used up anyway.
While obviously describing exactly what you want to do an establishing a whole "IF ELSE" tree would be absurd, just having the ability to take your turn later in that round at the cost of your reaction to otherwise simulate the hold action could potentially work.
