void start(int st){};

So the code could look something like this:

void start(int st)
{
  if(st==0)    
  {
     //Brightness decrement function here
  }else if(st==1)   
  {   
     //Brightness increment function here
  }
}    

For the brightness decrement function, it is the opposite of the increment function:

for (int i = 255 ; i >= 0; i--)
{
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
}

To summarize, the code could look something like this:

Why not create a global brightness variable (e.g. cBrightness) so that you can adjust the brightness accordingly when the time comes?

For the start() function, you can include one argument in the function to determine when to perform the brightening or dimming of the light.

void start(int st){};

So the code could look something like this:

#include <DS3231.h>

//Set Variables
int fadeTime = 15; //Fade Time
int onHour = 12; //Light On Hour
int onMin = 00; //Light On Minute
int offHour = 19; //Light On Hour
int offMin = 00; //Light On Minute
int led = 9; //Set pinout with with PWM
int cBrightness = 0;  //Current brightness

DS3231  rtc(SDA, SCL);
Time t;
void start(int st);

void setup()
{
  pinMode(led, OUTPUT);
  rtc.begin();
}

void loop()
{
  t = rtc.getTime();

  // Send Day-of-Week
  Serial.print(rtc.getDOWStr());
  Serial.print(" ");

  // Send date
  Serial.print(rtc.getDateStr());
  Serial.print(" -- ");

  // Send time
  Serial.println(rtc.getTimeStr());

  if (t.hour == onHour && t.min == onMin) //Check Time
  {
    start(1);
  }else if (t.hour == onHour && t.min == onMin)
  {
    start(0);
  }
  //Maintains brightness
  analogWrite(led, cBrightness);

}

void start(int st)
{
  if(st==0)     //Will decrement in brightness
  {
   for (int i = 255 ; i >= 0; i--)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
   cBrightness = 0;

  }else if(st==1)   //Will increment in brightness
  {   
   for (int i = 0 ; i <= 255; i++)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
  cBrightness = 255;
  }    
}

Why not create a global brightness variable (e.g. cBrightness) so that you can adjust the brightness accordingly when the time comes? With a global variable, you can still maintain the brightness of the LED even after it exits the start() function.

For the start() function, you can include one argument (int/bool type variable) in the function to determine when to perform the brightening or dimming of the light depending on the RTC timing.

void start(int st){};

So the code could look something like this:

#include <DS3231.h>

//Set Variables
int fadeTime = 15; //Fade Time
int onHour = 12; //Light On Hour
int onMin = 00; //Light On Minute
int offHour = 19; //Light On Hour
int offMin = 00; //Light On Minute
int led = 9; //Set pinout with with PWM
int cBrightness = 0;  //Current brightness

DS3231  rtc(SDA, SCL);
Time t;
void start(int st);

void setup()
{
  pinMode(led, OUTPUT);
  rtc.begin();
}

void loop()
{
  t = rtc.getTime();

  // Send Day-of-Week
  Serial.print(rtc.getDOWStr());
  Serial.print(" ");

  // Send date
  Serial.print(rtc.getDateStr());
  Serial.print(" -- ");

  // Send time
  Serial.println(rtc.getTimeStr());

  if (t.hour == onHour && t.min == onMin) //Check Time
  {
    start(1);
  }else if (t.hour == offHour && t.min == offMin)
  {
    start(0);
  }
  //Maintains brightness
  analogWrite(led, cBrightness);

}

void start(int st)
{
  if(st==0)     //Will decrement in brightness
  {
   for (int i = 255 ; i >= 0; i--)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
   cBrightness = 0;

  }else if(st==1)   //Will increment in brightness
  {   
   for (int i = 0 ; i <= 255; i++)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
  cBrightness = 255;
  }    
}