Usually programs that designed for interactive use (when they own terminal) disable interactive features (like history for UP/DOWN, completion for TAB) when used in pipe.
Emacs usually use pipes for external processes. So interactive features are disabled.
Even if you send TAB, your client program does not interpret it for you as you want.
You can read man/help for your program and try force interactive mode by providing command line switch (like --login for GNU Bash).
To send TAB eval:
(defun my-comint-send-string (string)
"Send string to comint buffers. Useful for *compilation* read-only buffer."
(interactive
(list (read-input "Type string: " nil 'my-comint-send-hist-list)))
(comint-send-string (get-buffer-process (current-buffer)) string))
(define-key XXX-mode-map [C-return] 'my-comint-send-string)
and use such key sequence: C-RET C-q TAB RET.
But this may not work if buffering is enabled for stdio of your program (to flush input you must send \n
too)...
Mostly same problem discussed at Bash autocompletion in Emacs shell-mode
NOTE M-x term use pseudo terminal so all interactive program work as desired. But in this mode you lose any Emacs editing capabilities...