Simply keep the input statement within a while loop that checks your criteria:
import random
letters = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l',
'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z',
'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N',
'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']
numbers = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
symbols = ['!', '#', '$', '%', '&', '(', ')', '*', '+']
print("Welcome to the PyPassword Generator!")
nr_letters = 0
nr_symbols = 0
nr_numbers = 0
while nr_letters + nr_symbols + nr_numbers < 8:
nr_letters= int(input("How many letters would you like in your password?
"))
nr_symbols = int(input(f"How many symbols would you like?
"))
nr_numbers = int(input(f"How many numbers would you like?
"))
password = []
password.extend(random.sample(letters, nr_letters))
password.extend(random.sample(symbols, nr_symbols))
password.extend(random.sample(numbers, nr_numbers))
random.shuffle(password)
finalPassword = ""
print(f"Here is you password: {finalPassword.join(password)}")