Tmux is a very helpful terminal multiplexer, meaning it can split your terminal into multiple panes. So, create two side by side panes, then one way of doing it is:
on the left, run your cmd | tee >(grep ‘denied’ > error.log)
on the right, run tail -f error.log
The tee process takes it’s standard in, and writes itbto both standard out, so you see all the lines, and the path it’s been given. The >(…) operator runs the grep in a subprocess, and returns the path to it’s standard input pipe, so grep receives every line, and writes the denied lines to a log file which you display with tail in the other pane.
Rather than using a file for error.log you could also use a named pipe in much the same way.