Creating public instance of class in another class's initialization
As it's now in the first example, it's local variable in Timer constructor.

In the second one you have to use member initializer list in constructor as there is no default constructor in your display class.

class Timer {
public:
    Timer(uint8_t CLK, uint8_t DIO)
    : display(CLK, DIO) // constructor's initializer list 
    {
        ...
    }
    void updateDisplay() {
        ...
        display.setSegments(displayData);
    }

    // member variable:
    TM1637Display display;
}