There is no real substitute, but sage will give an interesting complex flavor that complements most meats. If you are talking red meat, rosemary is good, especially with venison or lamb.

I found a substitute list that mentions savory as a substitute - for thyme, sage and rosmary.

I haven't tried savory at all ...

Try a variety of different things. Obviously nothing tastes exactly like thyme, but lots of things can you give a nice burst of interesting flavor.

Sage, rosemary, herbs de provence (especially in a wine sauce over your beef), all of these would be good choices.

I have a spice blend I love to put on beef that consists of ground mustard, chili powder, smoked paprika, onion powder, black pepper, and salt. Experiment with proportions to see what you like.

I know this is going to sound strange but when I was in culinary school I played around with a lot of different spices and I think you should try mint I loved the contrast that it added to the meat paired with other spices it was very tasty.

Oregano or basil add flavors similar to thyme. They also dry and store very well if you have a fresh supply that you want to save for later meals.