My HTC Desire snapped and I have contacts in there but my SIM is missing?

Snapped as in actually split in two?

If the phone is still operational and the contacts were saved to the phone, inserting another SIM will enable you access to those.

If your screen is completely damaged/it is nonoperational and the contacts were not saved to the SIM, then getting them back is relatively impossible.

If they were saved to the SIM card, getting them back will only work by retrieving the SIM. Getting another SIM with the same number wont work.

PS: A safer way of saving contacts is saving them to a cloud (An online saveplace reachable with an e-mail adress, from any device)