I just bought a Canon 4000D, which came with an external flash. However, the camera doesn't come with the center hotshoe contact and the flash only works with the center contact. Is there an adapter that allows this camera to work with third party flashes?
No, you will need a flash specifically designed to work with Canon's E-TTL system; that does include some, but definitely not all, third party flashes.
Whoever sold you this combination was frankly a bit naughty.
Yes. Kind of. Sandwiching either the Godox X1T-C (firmware updated to v27 or later for T7/T100 compatibility) or X2T-C transmitter between the camera and the flash, gives you the ability to fire the flash (see this youtube video). But because the flash is single pin, that's all the camera can tell it to do. It would be better to get a different flash if you want more than that (see below).
Canon removed the center sync contact from the hotshoe on three models: the T7 (2000D/1500D), the SL3 (250D/200D Mark II) and the T100 (4000D/3000D). And newer copies of the T7 appear to have the contact reinstated.
But both the T7 and T100 without the contact work with full TTL/HSS function with Godox TTL-capable flashes that have had their firmware updated for this comaptibility, and newer models that came out since the firmware updates were introduced. This includes the Godox TT350C (firmware v1.7), V350-C (firmware v1.1), TT685-C (v3.4), TT685 II-C, V860 II-C (v1.8), V860 III-C and V1-C models.*
If you do not want to buy a Godox flash, I would check for the following things:
- That the flash is Canon E-TTL II and HSS compatible. While this won't guarantee compatibility, lack of it will definitely make the flash incompatible (as you say, the only pin the foot will have is the one you don't have a contact to match).
- That the flash is firmware-upgradeable.
- That there's a firmware image specifically for 4000D compatibility.
- Usage reports on the internet that the combination works.
- Footnote: The SL3 is a special case, since not all the Godox firmware updates for T7 and T100 compatibility apply to the SL3. Mostly only the transmitter updates work for the SL3.