i have been told that external antenna only increases signal strength and not the range, for range you have to increase the antenna transmit output power too....

Antenna is a passive device so itself doesn't generate any power. What antennas do is radiating the power (feed from the AP) with specific pattern.

Well, roughly speaking, we can imagine radio coverage is like a constant volumetric balloon. The more power input, the bigger the balloon.

However, with the same input power, high gain antenna cannot make the balloon bigger. Instead, it concentrate the input power in special area and change the balloon's shape.

TL-ANT2415D is 15dbi omni antenna. It concentrate the radio wave at in horizontal direction. So the wireless coverage can reach farther horizontally while become weaker in vertical direction.

That's saying if you are planning to extend the wifi signal to your room upstairs, TL-ANT2415D is not suitable. Antenna has little help on penetrating walls too.

Also, if your AP has 3 antennas, replacing only one with the TL-ANT2415D won't achieve good result.