Is there a synonym for the phrase "card up his sleeve"?

You're probably looking for

ace in the hole
A secret advantage, or some kind of resource kept until needed. It refers to a high-value card in stud poker which is kept face down while bets are made.

TFD Online

The "hole card" in stud is the card that is dealt first and remains face down until a showdown occurs.

One (also informal) synonym is secret weapon:

someone or something that gives you a special advantage over your opponents, especially in business or politics
The show could be ABC’s secret weapon in the ratings war this fall.
_{Macmillan Dictionary}

There's a very similar phrase: "She still has a trick up her sleeve."

trick up (one's) sleeve

A secret plan, idea, or advantage that can be utilized if and when it is required. A reference to cheating at a card game by hiding a favorable card up one's sleeve. I've got a few tricks up my sleeve if he decides to pursue legal action against me.

(source: The Free Dictionary)

trump card:

an advantage that makes you more likely to succeed than other people, especially something that other people do not know about.

I read your question as if you are looking for a word instead of a phrase. Maybe the word is "resourceful". I understand that to describe someone who always comes out of situations as if he had had a card up his sleeve.