The Standards of Care create a general guideline of 3 months of therapy. Averaged out as once per week, that works out to about 12 sessions. 10 sessions sounds within the realm of reasonableness.
I know people's mileage may vary on following the Standards of Care, gate-keeping, informed consent or the usefulness of therapy. I'm not addressing that because that's not what the OP is asking.
To answer the question: A therapist who is trying to follow the SOC may ask for something similar to what you're suggesting. It doesn't sound like just an effort to get more money out of you, though with any professional, one never knows. If you want to keep using this therapist, she may be ok with you having several fewer sessions, if you spread them out more over time (e.g., seeing you every other week for the three months). That doesn't solve your timing issue if you want Hrt now; but it could save you some money. If you want to get Hrt sooner, then you'd prob need a different therapist or to go the informed consent route.