Pointer to array of objects in C++

Many answers, but nobody is suggesting to use std::vector.

You're leaking memory. There's no deletes to your news. In modern C++, we would use smart pointers, i.e. std::unique_ptr<Train> trains[10], which is an array of smart pointers. And more logically, we would use a pointer to a dynamically allocated array: std::unique_ptr<Train[]> trains(new Train[10]). However, much better would be to use std::vector<Train> trains.

Example

struct Time {
    int hour;
    int minute;
};

struct TimeSpan {
    int hours;
    int minutes;
};

TimeSpan operator- (Time const& lhs, Time const& rhs) {
    TimeSpan ts {
        lhs.hour - rhs.hour,
        lhs.minute - rhs.minute };
    if (ts.minutes < 0) {
        ts.minutes += 60;
        ts.hours -= 1;
    }
    // and need something for when hours < 0, i.e. 0:30 - 23:30
    // with the exception for the case that you actually want a negative timespan...
    return ts;
}

#include <iostream>
std::ostream& operator<< (std::ostream& os, TimeSpan const& ts) {
    os << ts.hours << " hours and " << ts.minutes << " minutes";
    return os;
}

#include <string>
struct Train {
    int number;
    std::string name;
    TimeSpan travelTime;

    Train(Time const& departure, Time const& arrival)
    : number{/*?*/1}
    , name{/*?*/"name"}
    , travelTime{arrival - departure} 
    {}
};

std::ostream& operator<< (std::ostream& os, Train const& train) {
    os << "Train nr. " << train.number
       << " named " << train.name
       << " has a travel time of " << train.travelTime;
    return os;
}

#include <vector>

int main(){
    std::vector<Train> trains;
    trains.emplace_back(Train{Time{2,30},Time{4,40}});
    trains.emplace_back(Train{Time{1,20},Time{5,30}});
    trains[0].number = 100;
    trains[0].name = "Jansadabti";
    
    for (auto const& train: trains) {
        std::cout << train << '\n';
    }
}

What you have used is an array of pointers to objects but the question says to use a pointer to an array of objects. I suppose this means the array has to be dynamically created as demonstrated below. Note that usually UPPERCASE names are usually used for constants, so I've changed the name to Train. Also, the purpose of a constructor is to initialize the members of a class, not to perform calculations. Use methods (TimeDiff()) for calculations:

#include <string>
#include <iostream>
class Train {
public: 
    int Train_Number;
    std::string Train_Name;
    int Arrival_Hr;
    int Arrival_Min;
    Train(int number, std::string name, int hr, int min) 
    :  Train_Number(number), Train_Name(name), Arrival_Hr(hr), Arrival_Min(min)  
    {
        //empty body since I have used a member initializer list
    }
    Train() {} //empty constructor to allow array creation
    void TimeDiff(int new_hr, int new_min, int& diff_hr, int& diff_min)
    {
        diff_hr = new_hr - Arrival_Hr;
        diff_min = new_min - Arrival_Min;
    }
    // Overloading << so that you can use Train objects with std::cout
    friend std::ostream& operator<<(std::ostream& out, Train train);
};

std::ostream& operator<<(std::ostream& out, Train train)
{
    out << "\nTrain No: " << train.Train_Number;
    out << "\nTrain Name: " << train.Train_Name;
    out << "\nArrival Time: " << train.Arrival_Hr << ":" << train.Arrival_Min;
    return out;
}
int main()
{
    Train* t_array;
    t_array = new Train[10]; // Dynamically allocates a dynamic array of size 10 and returns a pointer to the base address

    t_array[0].Train_Number = 100;
    t_array[0].Train_Name = "Jansadabti";
    t_array[0].Arrival_Hr = 2;
    t_array[0].Arrival_Min = 30;
    //OR
    t_array[0] = Train(100, "Jansadabti", 2, 30);

    int diff_hr, diff_min;

   
   std::cout << t_array[0] << std::endl; // Possible because << is overloaded
   std::cout << "New Time: " << 4 << ":" << 40 << std::endl;

   t_array[0].TimeDiff(4, 40, diff_hr, diff_min);
   std::cout << "Time Difference: " << diff_hr << "hr " << diff_min << "min ";
    
     delete[] t_array; // Always delete dynamically allocated memory.
    return 0;
}

If something is not clear, do let me know, I'll break it down for you. Also, try to not use using namespace std, it clutters the global namespace. At the end of the day, it's C++, where someone will always complain about your code not being optimal enough.