Just because I always forget and the parameters are somewhat non-trivial, here’s how you start an xterm inside X:

startx $(which xterm) -- :0 vt01

Of course, the display name :0 is usually used by default, so you may need to use another one (:1 etc.) if you get an error like “Server is already active for display 0“. You can also select a different virtual terminal.

Note that the absolute path to xterm (or whatever application you’d like to start inside X) is essential.