If TSH is normal or slightly elevated and T4 is low this suggests hypopituitarism. Take blood for cortisol and ACTH and then give hydrocortisone replacement before starting levothyroxine and investigate for hypopituitarism.
Levothyroxine, oral, 100 mcg daily.
If there is a risk of ischaemic heart disease, start at 25 mcg daily and increase by 25 mcg every 4 weeks.
Check TSH and T4 after 2-3 months and adjust the dose if required.
TSH levels will take several weeks to stabilize. Once stable check T4 and TSH annually.