Rock, Paper, Scissors Game in Python
I would use a dictionary to store the choices, and pass the input through capitalize() so, the user doesn't have to write the capitalized word(i am doing this only because you have it that way, but unless you are printing the word as it is, i recommend you to use only lowercase or uppercase to avoid unmatching), also, the while loop is unnecesary because you are calling play() if the user wants to play again.

def play():
    p_choice = input("What do you choose?").capitalize()
    choices = {1 : 'Rock', 2 : 'Paper', 3 : 'Scissors'}
    cpu_choice = choices[random.randint(1,3)]


then, you can do the same thing for all cases, instead of all those conditionals, you can build a dictionary for all cases and then let the compare function return True if its a win or False if its a lose, although i wouldn't recommend you to define the function inside play()

def compare(playerChoice,cpuChoice):
    results = {('Paper','Rock') : True,
               ('Paper','Scissors') : False,
               ('Rock','Paper') : False,
               ('Rock','Scissors') : True,
               ('Scissors','Paper') : True,
               ('Scissors','Rock') : False}
    return results[(playerChoice,cpuChoice)]


and this is my version of game_start()

def game_start():
    begin = input("Would you like to play Rock, Paper, Scissors? ").capitalize()
    while begin != "Yes":
        if begin == "No":
            print("Game Over")
            return sys.exit()
        else:
            print("Please try again")
            begin = input("Would you like to play Rock, Paper, Scissors? ").capitalize()
    play()
    while True:
        begin = input('Play again?').capitalize()
        while begin != "Yes":
            if begin == "No":
                print("Game Over")
                sys.exit()
            else:
                print("Please try again")
                begin = input("Play again? ").capitalize()
        play()


the whole code looks now like this:

import random
import sys

def play():
    p_choice = input("What do you choose?").capitalize()
    choices = {1 : 'Rock', 2 : 'Paper', 3 : 'Scissors'}
    cpu_choice = choices[random.randint(1,3)]
    if p_choice == cpu_choice:
        return print('Tie!')
    if compare(p_choice,cpu_choice):
        return print('You Win!')
    else:
        return print('You Lose!')

def compare(playerChoice,cpuChoice):
    results = {('Paper','Rock') : True,
               ('Paper','Scissors') : False,
               ('Rock','Paper') : False,
               ('Rock','Scissors') : True,
               ('Scissors','Paper') : True,
               ('Scissors','Rock') : False}
    return results[(playerChoice,cpuChoice)]

def game_start():
    begin = input("Would you like to play Rock, Paper, Scissors? ").capitalize()
    while begin != "Yes":
        if begin == "No":
            print("Game Over")
            sys.exit()
        else:
            print("Please try again")
            begin = input("Would you like to play Rock, Paper, Scissors? ").capitalize()
    play()
    while True:
        begin = input('Play again?').capitalize()
        while begin != "Yes":
            if begin == "No":
                print("Game Over")
                sys.exit()
            else:
                print("Please try again")
                begin = input("Play again? ").capitalize()
        play()

game_start()