There are two aspects to consider based on your exposition: hardware and software.
AP Hardware: since you have one USB port only you need to use a USB hub in order to increase the number of available ports.
AP Software: the AP should be able to manage both devices, the printer and the external HD.
My recommendation is to confirm that your AP can manage both devices alone that is, without the USB hub. You would need to connect the printer and confirm the AP can manage it and also that your laptop can connect and print to it. Then the same thing with the external HD that is, connect the HD alone, confirm it can be managed by the AP and then confirm it can be accessed by your laptop.
Once the above gets confirmed, go ahead and install the USB hub. Start connecting one device at the time and confirm its accessibility from your laptop.
I had this exact same configuration working problem free -but slow, on a old Asus AP featured with one USB port only.