1326 starting hold'em combos

Jelly, 21 bytes

9Ḋ;“TJQKA”Ṛp“cdhs”ŒcK

A full program printing the combos* separated by spaces (as a niladic link without the trailing K the result would be a list of combos, where each combo is a list of lists, with integers for 2-9 and characters for other parts).

Try it online! (Note: change the trailing K to L and it will display the length of the list, 1326.)

How?

9Ḋ;“TJQKA”Ṛp“cdhs”ŒcK - Main link: no arguments
9Ḋ                    - nine dequeued               [2,3,4,5,6,7,8,9]
   “TJQKA”            - literal list of characters  ['T','J','Q','K','A']
  ;                   - concatenate                 [2,3,4,5,6,7,8,9,'T','J','Q','K','A']
          Ṛ           - reverse                     ['A','K','Q','J','T',9,8,7,6,5,4,3,2]
            “cdhs”    - literal list of characters  ['c','d','h','s']
           p          - Cartesian product           [['A','c'],['A','d'], ... ,[2,'s']]
                  Œc  - Unordered pairs             [[['A','c'],['A','d']], ...(1326)...]
                    K - join with spaces (to pretty print, otherwise they all run
                      -   together like AcAdAcAhAcAsAcKdAcKhAcKs...2d2h2d2s2h2s)

* it's what the kids call 'em!

Python 2, 100 98 bytes

r=range
d=lambda i:'AKQJT98765432'[i/4]+'cdhs'[i%4]
for u in r(52):
 for t in r(u):print d(t)+d(u)

-2 bytes from dylnan

Try it online!

d maps the numbers from 0 to 51 to card names such that they keep their sorting order (0-3 -> Aces, 4-7 -> Kings, etc)

The program loops over all pairs of numbers 0-51 where the second is greater than the first, and prints the pair of cards corresponding to that pair of numbers.