How to get the gain of the antenna with different excitatioin power?

I am co-designing my antenna with amplifiers.

I know that the antenna's gain is a intrinsic characteristic of the antenna independent upon the input power. I am wondering how can I apply the output of the amplifier (like 10 dBm) to the antenna to calculate the antenna's gain under the specific input power, which simulate the real case in antenna gain measurement. The default excitation power of a single port in HFSS is 1W.

Antenna gain is directly related to directivity; both mean that the antenna, instead of spreading the RF power to all spatial angles equally (omnidirectional antenna), directs most of power into a desired direction while suppressing the radiation into other directions.
Including an amplifier does not change anything as the above directivity is purely geometrical. What the amplifier gain does affect is EIRP, the power level directed to the desired point.

I am wondering how I can apply the specific output power of the amplifier to the antennas' input port.

Just connect it there! Make sure the impedances are matched, it will work.

do you know what the output of your amplifier is ?
have you actually measured it on a dummy load Wattmeter ?

if so, then you know how much power you are applying to the antenna
minus any losses in the feedline

Dave