Cannot move TM1637 from Uno to Pro Mini
Since you're using a Grove Display, I believe it will be using I2C.

For better debugging, try using the actual I2C pins on your Pro mini, which are A4 and A5.


  I2C: A4 (SDA) and A5 (SCL). Support I2C (TWI) communication using the
  Wire library.
  https://www.arduino.cc/en/Main/ArduinoBoardProMini


I2C may need pull-up resistors on your data lines.

(https://en.wikipedia.org/wiki/I%C2%B2C)

It can also be nice to use "verified to be working" code, like example code from the manufacturer.

/*
 * TM1637.cpp
 * A library for the 4 digit display
 */
#include "TM1637.h"
#define CLK 39 //pins definitions for TM1637 and can be changed to other ports
#define DIO 38
TM1637 tm1637(CLK,DIO);
void setup()
{
    tm1637.init();
    tm1637.set(BRIGHT_TYPICAL);//BRIGHT_TYPICAL = 2,BRIGHT_DARKEST = 0,BRIGHTEST = 7;
}
void loop()
{
    int8_t NumTab[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};//0~9,A,b,C,d,E,F
    int8_t ListDisp[4];
    unsigned char i = 0;
    unsigned char count = 0;
    delay(150);
    while(1)
    {
        i = count;
        count ++;
        if(count == sizeof(NumTab)) count = 0;
        for(unsigned char BitSelect = 0;BitSelect &lt; 4;BitSelect ++)
        {
            ListDisp[BitSelect] = NumTab[i];
            i ++;
            if(i == sizeof(NumTab)) i = 0;
        }
        tm1637.display(0,ListDisp[0]);
        tm1637.display(1,ListDisp[1]);
        tm1637.display(2,ListDisp[2]);
        tm1637.display(3,ListDisp[3]);
        delay(300);
    }
}


You will need to adapt the pin numbers.

But after these steps it should work just fine.

Source: http://wiki.seeed.cc/Grove-4-Digit_Display/