My mom has had diabetes for four years. She taking Glimepiride tablets, 1 mg, and Metformin tablets, 500 mg in the morning and evening. Recently, she had blood work, which indicated thyroid issues. Two weeks ago, she started Synthroid, 75 mcg (Levothyroxine sodium, 75 mcg) once a day. She checked her fasting blood sugar level at home this morning and it was 9.6 mmol/L (173 mg/dL). Why was sugar level this high? Is it related to the thyroid
medicine? Before, her blood sugar was 7.9 mmol/L (142 mg/dL). Does she need to see the doctor urgently?

This is probably not something urgent. It seems like she may need some additional medications to help lower her blood glucose levels. Type 2 diabetes is something that progresses for most people, and what tends to happen is that people start out on some oral medications, which can work well for some people if it is combined with dietary and exercise modifications for a long time. For others, it only works for a shorter time. Here is some more information on type 2 diabetes progression:
http://www.diabetesforecast.org/2015/sep-oct/type-2-diabetes-progression.html

The thyroid medication should have no effect on the blood glucose
levels. However, if she is hypothyroid and now is working to get to
normal thyroid levels, it may actually help her blood glucose levels
normalize slightly. The thyroid hormones help regulate metabolism and
blood glucose levels in that way. Here is some more information:
https://www.verywellhealth.com/thyroid-disease-and-diabetes-3289616