Short Answer: Yes, but they are usually temporary or overcome by prescription adjustments.
As with any drug, there are known short-term and usually mild side effects from estrogen or progestogens which may cause trouble for some, especially in the first few months of use. These may include breast tenderness, leg cramps, nausea, bloatedness, irritability, or depression. These side effects are related to changes in estrogen or progestogens and may be overcome by giving your body time to adjust to the change (give it at least one month after any HRT change!), or by changing the dosage, ingredients, or delivery method of the hormones prescribed.
It is helpful to track any anticipated symptoms or side effects daily so that you can monitor how responses to your HRT might change over time or in response to any adjustments made by your doctor. remember, give any change at least one month, since studies show that side effects can resolve on their own once your body has adjusted to the new level of hormones (particularly in PMDD).
If you still have your uterus, irregular bleeding or spotting can occur during the first 4-6 months of taking continuous combined estrogen and progestogen and is not a cause for alarm. However, you should consult your doctor if you get heavy (rather than light) bleeding, if it continues for more than six months, or if bleeding starts suddenly after some time without bleeding. Irregular bleeding may sometimes be improved by changing the type or route of hormones.
NAMS 2017 Hormone Therapy Position Statement (North America)